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We study the emergence and nature of long-run behavior of continuous state space dynamics that are subjected to random shocks. It is shown that the fine details of the underlying deterministic dynamics may be crucial in determining the evolution of the system. In particular, a risk dominated strategy can emerge in an evolutionary game subject to symmetric decaying perturbations.

We propose a theory of party competition (two parties, single-issue) where citizens acquire party membership by contributing money to a party, and where a member’s influence on the policy taken by her party is proportional to her campaign contribution. The polity consists of informed and uninformed voters: only informed voters join parties, and the party campaign chest, the sum of its received contributions, is used to reach uninformed voters through advertising. A party is a cooperative organization of its members. Parties compete with each other strategically with respect to policy choice and advertising. We propose a definition of political equilibrium, in which party membership, citizen contributions, and parties’ policies are simultaneously determined, for each of four financing institutions, running the gamut between a purely private, unconstrained system, to a public system in which all citizens have equal financial input. Equilibria under these institutions are computed by simulation for an example. The representation and welfare properties of these four institutions are compared from these simulations.

This paper studies mutual consent social networks in which individuals imperfectly monitor others' network ties and have incomplete information about the benefits of network participation. I introduce the Conjectural Pairwise Stability concept, which generalizes Jackson and Wolinsky's (1996) Pairwise Stability concept to allow for limited observation, and apply it to a specific mutual consent network formation game. While limited observation generally leads to the existence of less efficient stable networks, I find that it can also lead to the existence of efficient stable networks. Moreover, stability restrictions considered in previous work lose their refining power as observation becomes more limited.

This paper examines the consequences of status preferences on entrepreneurial risk-taking in a general equilibrium model of occupational choice. We distinguish between two frames of reference. In the first, status is derived from class-membership, the economic indicator of which is the expected relative income of the person's occupation. In the second, status is tied to individual income relative to the mean. We find that the effect of status needs depends on whether or not the status variable itself is subject to risk. While social status increases entrepreneurial risk-taking in the first case, the effect is ambiguous in the second and crucially depends on how status preferences alter the effective degree of risk aversion. The results carry over to the distributional consequences, where status preferences have an equalizing effect only if certain conditions are met.

This paper considers the problem of an agent's choice under uncertainty in a new framework. The agent does not know the true probability distribution over the state space but is objectively informed that it belongs to a specified set of probabilities. Maintaining the hypothesis that this agent is a subjective expected utility maximizer, we address the question of how the objective information influences her subjective prior.Three plausible rules are proposed. The first, named state independence, states that the subjective probability should not depend on how the uncertain states are `labeled'. Location-consistency, the second property, assumes that `similar' objective sets of probabilities result in `similar' subjective priors. The third rule is an `update-consistency' rule. Suppose the agent selects some probability p. She is then told that the likelihood assigned by p to some event A is in fact correct; then this should not cause her to revise her choice of p.Another property, alternative to update-consistency, is also proposed. When an agent forms her subjective prior assigning subjective probabilities to events in some ordered sequence, this property requires that the resulting prior be independent of that order. This last property, named order independence, is shown to be equivalent to update-consistency.A class of sets of probabilities is found on which state independence, location-consistency and update consistency (order independence) uniquely determine a selection rule. Some intuition is given regarding why these properties work in this collection of problems.

We propose a novel approach to modelling time preferences, based on a cognitive shortcoming of human decision makers: the perception of future events becomes increasingly `blurred' as the events are pushed further in time. Our model explains behavioural `anomalies' such as preference reversal and cyclical choice.

A rational bidder in a private-value auction should be reluctant to incur the cost of perfectly estimating his value if it might not matter to the success of his bidding strategy. This can explain sniping---flurries of bids at the end of auctions---as the result of other bidders trying to avoid stimulating the victim into learning more about his value. The idea of value discovery also explains why a bidder might increase his bid ceiling in the course of an auction and why he would like to know the private values of other bidders.

The paper characterizes the optimal provision of quality by a monopolist facing a population of consumers with private valuation for quality. Unlike previous models by Mussa and Rosen (1978) and others, this paper assumes there is a mass of consumers who prefer the highest quality goods. I liken these consumers to snobs who demand the highest valued goods. I show that the quality supplied jumps discontinuously as the highest valued consumers are encountered and the variety of products is reduced as the population of snobs increases. I also show that only snobs may be supplied once their population grows to a critical size.

This paper provides a general framework for pricing of real options for wide classes of payoff streams that are functions of Levy processes. As applications, we calculate the values of sequences of embedded options, (which we call Russian dolls), and study two models of expansion of a monopoly. In the first model, the monopoly increases capital stock each time the stochastic demand crosses the boundary of the inaction region. Assuming that above a certain level, the stochastic demand factor increases slower than in the standard geometric Levy models, we demonstrate that the investment threshold is lower than in the standard models. Moreover, in the intermediate range between the regimes of the fast and slow growth, the monopoly may find it optimal to simultaneously increase the capital stock and decrease the output price. In a two-factor model of technology adoption, we show that diffusion and jump uncertainty can produce opposite effects.

Within a costly state verification setting, we derive the optimal financial contract between an entrepreneur, a (potentially financing) supervisor and a pure investor when there is non-verifiable and non-contractible monitoring and limited liability. We show that diversion of cash flows to the entrepreneur arises as optimal behaviour and that to get the best reporting and monitoring incentives it is crucial to separate the financing from the monitoring role. In particular, higher efficiency can be achieved by ensuring that the entrepreneur and the supervisor do not collect any cash flows in low states. These should be paid to a third party instead, the pure investor, who in exchange provides funding. However, whether the pure investor entirely finances the project (and the supervisor purely acts as a monitor) or only provides partial finance (with the supervisor cofinancing) is immaterial, as the optimal financing of the project can justify a range of alternative financial structures.

A bilateral trading model with investment is considered. In a “cooperative” investment version of the model, the seller's investment stochastically determines the buyer's valuation of the good. The value and cost of the good are realized only after the investment is made, and the investment level and the realization of the good's value and cost are private information. I show that, under these assumptions, no contract made before the investment can simultaneously induce efficient investment and efficient ex post trade when the buyer's type is continuously distributed. This inefficiency result contrasts sharply with the efficiency result under the standard “selfish” investment model, where the seller's investment stochastically determines the seller's cost.

This paper extends the Downsian-Hotelling model of electoral competition to allow for unobserved qualitative differences between candidates. I show that these underlying qualitative differences generate pure strategy Nash equilibria, even if policies are defined in a multidimensional space, and explain platform divergence from the median. Moreover, the extension gives content to a second (well-known) role elections play apart from bridging conflict: to reveal information about candidates.

Does economic justice stymie economic development? This paper demonstrates that sustainability is compatible with Rawlsian intertemporal justice, even when considering human capital and natural resources. The methodology employed herein extends and amends previous works that (1) do not consider human capital or renewable resources, and (2) rely upon the application of standard Lagrangian methodology to a continuum of nonlinear constraints. This approach circumvents problems associated with earlier works by internalizing constraints and demonstrating two sufficient conditions which guarantee existence of a Rawlsian maximin path.

This paper studies the relationship between competition and incentives in an economy with financial contracts. We concentrate on non-exclusive credit relationships, those where an entrepreneur can simultaneously accept more than one contractual offer. Several homogeneous lenders compete on the contracts they offer to finance the entrepreneur's investment project. We model a common agency game with moral hazard, and characterize its equilibria. As expected, notwithstanding the competition among the principals (lenders), non-competitive outcomes can be supported. In particular, positive profit equilibria are pervasive. We then provide a complete welfare analysis and show that all equilibrium allocations turn out to be constrained Pareto efficient.

This paper analyses conditions on agents' preferences for a unique stable matching in models of two-sided matching with non-transferable utility. The No Crossing Condition (NCC) is sufficient for uniqueness; it is based on the notion that a person's characteristics, for example their personal qualities or their productive capabilities, not only form the basis of their own attraction to the opposite sex but also determine their own preferences. The paper also shows that a weaker condition, alpha-reducibility, is both necessary and sufficient for a population and any of its subpopulations to have a unique stable matching. If preferences are based on utility functions with agents' characteristics as arguments, then the NCC may be easy to verify. The paper explores conditions on utility functions which imply that the NCC is satisfied whatever the distribution of characteristics. The usefulness of this approach is illustrated by two simple models of household formation.

Conditional on the considered equilibrium, the probability of a bank run in the demand-deposit contract models of Bryant (1980) and of Diamond and Dybvig (1983) is either one or zero. In contrast, we establish the existence of an interval - being a strict subset of the unit-interval - of possible bank run probabilities for a two-player demand-deposit contract model where players receive independent signals about their liquidity desire from a continuous type space. As our main result we demonstrate that this interval reduces to a unique probability of a panic-based bank strictly smaller than one if and only if there exist types for which not running on the bank is a dominant action. In addition to existing models of bank runs such as, e.g., Goldstein and Pauzner (2005), our approach also provides some assessment of the likelihood of a bank run if there are no types for which not running on the bank is a dominant action. As a consequence, we can investigate the comparative statics of the likelihood of bank runs with respect to a larger range of payoff parameters than considered in previous models. Furthermore, we derive a technical result by which the findings of Morris and Shin (2005) on the dominance-solvability of binary action games with strategic complements also apply to nice games in the sense of Moulin (1984) if players' best response functions are increasing.

We study a model with product differentiation by manufacturers and spatial differentiation by supermarkets where the customers visit only one shop and the supermarkets carry both goods. Under fixed fee pricing by the manufacturers the intensity of interbrand competition increases with the degree of differentiation between the supermarkets. When the supermarkets are more and more spatially differentiated the struggle between manufacturers and supermarkets dominates the competition between the manufacturers and results in lower wholesale prices and manufacturers profits.

Several studies have recently adopted the segmented markets model as a framework for monetary analysis. The characteristic assumption is that some households never participate in financial markets. This paper proves the existence of an equilibrium for segmented markets models where monetary policy is defined in terms of the short-term nominal interest rate. The model allows us to consider the important cases where monetary policy affects output, and responds to any sources of uncertainty, including output itself. The assumptions required for existence constrain the maximum value and the variability of the nominal interest rate. The period utility function is logarithmic. The proof is constructive, and shows how the model can be solved numerically. A similar proof can be used in the case that monetary policy is defined in terms of the bond supply.

I study affiliated, pure common-value auctions with ex-ante asymmetric buyers. For the two-buyer case I characterize and prove uniqueness of the equilibrium of hybrid auctions where the payment is a weighted average of the highest and second-highest bids. A recursive method to explicitly compute the equilibrium is presented. It is shown that any hybrid auction yields at least as much revenue as the first-price auction. In particular, the equilibrium of the second-price auction, obtained in the limit by letting the weight of the highest bid go to zero, revenue-dominates the first-price auction.

This paper analyzes the dynamics of completely decentralized bilateral exchange. In such a framework, neither money nor prices as public information exist. Rather, prices represent an agent's barter strategy, and hence are private information. We call these private prices. Agents formulate trade offers and accept or reject offers from other traders, on the basis of their private prices. Private prices are updated by low-scoring agents periodically imitating the strategies of higher-scoring agents. We show that a system of quasi-public prices emerges in the medium run, and these quasi-public prices converge to stationary distributions that are approximately competitive equilibria of the underlying Walrasian model in the long run. We thus provide, for the first time, a general, decentralized disequilibrium adjustment mechanism that renders market equilibrium dynamically stable in a highly simplified production and exchange economy.

A distributed system model is studied, where individual agents play repeatedly against each other and change their strategies based upon previous play. It is shown how to model this environment in terms of continuous population densities of agent types. A complication arises because the population densities of different strategies depend upon each other not only through game payoffs, but also through the strategy distributions themselves. In spite of this, it is shown that when an agent imitates the strategy of his previous opponent at a sufficiently high rate, the system of equations which governs the dynamical evolution of agent populations can be reduced to one equation for the total population. In a sense, the dynamics 'collapse' to the dynamics of the entire system taken as a whole, which describes the behavior of all types of agents. We explore the implications of this model, and present both analytical and simulation results.

We analyze endogenous lobby formation within a slightly modified version of the "special interest politics" model of Persson (1998). In our model the interest groups hold different fixed endowments of an "infrastructure good" which is a complement in consumption of the local public good. For any fixed set of organized groups the lobbying game is shown to have a unique equilibrium if the cost-elasticity of the supply of public good to the interest groups by the government is not too large. The groups which benefit from larger infrastructure endowments are then proved to be the ones which become organized while the others remain unorganized.

We analyze two robust portfolio selection models, where a mean-variance investor considers possible deviations from a reference distribution of asset returns, adopting a maxmin criterion. The two models differ in the metric used to measure the distance between the reference distribution of asset returns and the alternative probability distributions. In the first model, where relative entropy is used as a measure of distance between distributions, an observational equivalence result obtains, whereby introducing robustness is equivalent to increasing risk aversion and, therefore, the percentage composition of the optimal portfolio of risky assets is equal to that of the optimal portfolio held by an investor without concerns for robustness. In the second model, introducing an alternative measure of distance between distributions, we show that observational equivalence ceases to hold and the proportions between risky assets are altered. We exploit the natural game-theoretic interpretation of the maxmin setting to illustrate the differences between the two models.

Analyses of risk-bearing often assume that agents face only one risk. Agents however usually face several risks and the interaction between them can affect the willingness to bear any one of them. We consider how the introduction of background risk affects the comparative statics predictions of distribution changes in the standard two asset portfolio model. We show that such predictions are fairly robust, no matter what the correlation between the two risks. We consider changes in the conditional distributions of the risky asset's return; and changes in the marginal distribution of the asset's return. For the first question, a version of Gollier's (1995) Central Riskiness order is sufficient and necessary to increase risk-bearing. For the second question, Monotone Likelihood Ratio improvements are sufficient and necessary. Many of our proofs illustrate the "basis" approach to comparative statics under uncertainty.

This paper extends models of renewable resources to an economy with two sectors, resource extraction and production. In contrast to one sector models, we show that the optimal strategies in the single-firm model are essentially different from those in the two-player model. In the single-player model, the optimal strategy is to keep the resource extraction a constant multiple of production labor. In the two-player model, the optimal strategy for each player is to keep extracting labor a constant multiple of production labor. It is also shown that the extraction-to-production labor ratio is increasing with the wage and the interest rate and is decreasing with the production TFP, the extraction TFP, and the stock level in the single-player model, but not in the two-player model. Finally, I show that another way for each firm to maximize profit is to raise its zero-profit stock level by maximizing its geometric average TFP.

This paper considers the optimality of setting a secret reserve price in ascending auctions. Contrary to intuition, an ascending auction is no longer equivalent to a second price auction when the reserve price is secret. We determine the seller's optimal reserve price policy when the bidders' values are private and independently distributed and when the bidders are risk averse. We show that an optimal secret reserve price policy can dominate an optimal public reserve price policy when the bidders' degree of constant relative risk aversion is sufficiently high and when the seller can commit to a reserve price policy before learning her type. In contrast, a secret reserve price policy can never be part of a Bayesian equilibrium when the seller is informed.

This paper develops a model of terrorist activity and behavior. A terrorist organization chooses the size and the number of attacks. The defending state chooses the level of security-deterrence measures. The equilibrium sequence is such that the Organization moves first, followed by the State. A defensive policy such as an innovation in security-deterrence technology tends to reduce the size of attacks but increase their number, while an offensive policy, lowering the total "strike" or "output" potential of a terrorist organization, has opposite effects. Both policies reduce the expected damage from terror. An individual's decision to become a terrorist or a financier is also modeled, leading to endogenous supplies of terrorists and funds. The effects of terrorist-flushing measures, provisions to curb the flow of funds to terrorist organizations and income-enhancing policies are evaluated by taking into account their "supply-side" effects.

Allaz (1992) and Allaz and Vila (1993) show that in an oligopolistic industry the introduction of a futures market that operates prior to the spot market induces more competitive outcomes. Hughes and Kao (1997) show that this result presumes that firms' future positions are perfectly observed, and that when firms' positions are not observed the Cournot outcome arises. We study an alternative formulation of observability, where the behavior of participants in the futures market is explicitly analyzed, and show that this approach leads to different results. Imperfect observability induces more competitive outcomes than Allaz and Vila's model.

In order to incorporate demand interdependencies into the analysis of fairness between the different consumer groups of a multi-product public utility, Baumol (1986) designed the burden test. This test checks whether the price of a single good generates net incremental revenues which cover at least the incremental costs of the good. It is, however, more reasonable to compare net incremental revenues and net incremental costs. Furthermore, it is useful to extend the analysis to groups of goods. Therefore, we develop a new fairness test, which we call the net burden test, and characterize its properties.

This paper characterizes the utility possibility frontier resulting in a model of private voluntary provision of a public good. It is shown that ex-ante lotteries over resource distributions among the agents can be Pareto improving. A corollary is that an equal distribution of resources among the agents, or any distribution where all agents contribute in equilibrium, is always Pareto dominated by a lottery between two unequal distributions.

This paper shows that favoritism can arise endogenously as an optimal decision rule in a symmetric model with an ex-ante impartial principal. Furthermore, favoritism dominates fairness specifically when the favorite promotes his own idea and ignores the other's idea so that the non-favorite loses motivation. Our model also provides new insights on hierarchical communication structure and group authority.

Across countries, government expenditures tend to favor the elderly. This paper provides a political economy explanation for this phenomenon. I consider the classic problem of dividing a fixed payoff in an overlapping generations setting. Any share of the payoff can be given to any generation. Using a new solution concept for majority rule in dynamic settings (Bernheim and Slavov, 2006), I demonstrate that policies favoring the old are easier to sustain politically than other policies. This result appears across a broad class of majoritarian institutions and thus reflects general forces at work in the political process. Age bias arises because it is easy to induce the young to support policies favoring the elderly by promising them large rewards later in their lives. On the other hand, older generations cannot be rewarded in a similar manner. This asymmetry helps to generate broad political support for large transfers to older individuals.

R&D is typically characterized by uncertainty about the existence and timing of the innovation (``fundamental R&D"). I show that these uncertainties dampen R&D investment, which may exhibit non-monotonic dynamics, possibly converging to a steady state level. In fundamental R&D, increased rivalry raises investment in the short run, but dampens it in the long run. With an endogenous market structure and free entry, perfect competition ensues, where the race lasts for an instant; with costly entry, firms engage in R&D only if they’re sufficiently optimistic that the innovation exists. Previous models of R&D races, which assume timing uncertainty (``secondary R&D"), are special cases of this model, which allows for a comparative analysis of fundamental and secondary R&D race environments.

In an ongoing organization, such as a large law partnership firm, employees are motivated not only by current rewards but also by the prospect of promotion, and the opportunity to make the rules in the future. This leads to a recursive contract design problem in an overlapping generations environment, where current agents may become future principals. The principal offers, and promotion-motivated agents accept, harsh rat race contracts with low wages and high effort levels. Hiring and promotion probabilities emerge as the preferred instrument to screen high cost workers, who face employment barriers and a glass ceiling.

This paper shows that in a contest with the "Tullock" forms of contest success function, an increase in the number of contestants always reduces individual effort. However, when the outcome of the contest is governed by a noisy function of effort, then individual effort could either increase or decrease following an increase in the number of contestants, depending on whether the density function of the shock is upward or downward sloping.

In this paper, we consider an incumbent firm facing potential entry in a vertical differentiation model a la Mussa and Rosen where consumers differ only by their intensity of preference for quality. We ask whether the incumbent firm has the incentive to adopt a multi-product strategy in order to face entry, in a natural duopoly case. It turns out that this strategy is never profitable and that an incumbent always prefers to produce one quality. It appears that either a cost effect or an income dispersion are necessary to urge producers to offer several products.

We present a model of cooperative production in which rational agents might carry out sabotage activities that decrease output. We provide necessary and sufficient conditions for the existence of a Nash equilibrium without sabotage. It is shown that the absence of sabotage in equilibrium depends on the interplay between technology, relative productivity of agents and the degree of meritocracy. In particular we show that, ceteris paribus, meritocratic systems give more incentives to sabotage than egalitarian systems.

This paper analyzes equilibria in sequential take-it-or-leave-it sales when demand is stochastic. It is shown that equilibria in this sales mechanism, unlike in sequential auctions, trade-off allocative efficiency and competing buyers' opportunities to acquire an item to be sold, permitting prices and expected revenue above those of one-shot offers. Hence Coase-type conjectures are invalid in this setting.

This paper focuses on the signalling role of debt maturity. The main novelty of the paper is that it analyzes a setting in which high quality firms use collateral as a complementary device along with debt maturity to signal their superiority. Model simulations suggest a non-monotonic relationship between firm quality and debt maturity, in which high quality firms have both long-term secured debt and short-term secured or non-secured debt and low quality firms have long-term unsecured debt. We provide some empirical evidence for this result based on debt contracts of the Asia Commercial Bank.

If Cournot oligopolists face uncertainty about the intercept of a linear demand function and if the realized market price must be non-negative, then expected demand becomes convex, which can create a multiplicity of equilibria. This note shows that if the distribution of the demand intercept has a monotone hazard rate and if another, rather weak, assumption is satisfied, then uniqueness of equilibrium is guaranteed.

We consider a monopoly producing a good whose demand grows over time. Whatever the price policy which is adopted, the monopolist invests in order to meet the resulting demand growth. She can only invest in indivisible factory units. We identify the optimal price policy, and the ensuing optimal sequence of investment time points the monopoly selects through time. We show that this sequence satisfies the constant cycle property observed under capacity expansion for an exogenous increase in demand (Manne, 1961).

In a sharing game the players' choices yield a revenue, each player's choice carries a cost, and a player's payoff is a portion of the revenue minus the player's cost. Such games are appealingly simple devices for partially aligning individual incentives with organizational goals, but their equilibria may be inefficient, i.e., at an equilibrium the surplus (revenue minus the sum of the costs) may not be maximal. Sharing games as a general class have not been well studied. We start a general theory of sharing games by going beyond the common economic setting, where strategy sets are continua and cost and revenue functions are smooth. We include games in which some of a player's strategies are equally costly, and revenue changes when he switches from one of them to another. We consider several large classes of reward functions, including nondecreasing residual (NDR) functions, in which residual (revenue minus rewards) does not drop when revenue increases. That class includes budget-balancing functions, where residual is always zero. To focus the discussion, we examine a ``Folk Claim", which asserts that at every inefficient equilibrium shirking, in some sense, occurs. We show that in NDR games a complementarity condition indeed insures that no one squanders at equilibrium (spends more than at an efficient profile). But when we drop complementarity, the situation changes sharply, and there are games with compelling equilibria, at which some players squander. The shirking/squandering distinction is particularly important in tracing the effect of technical improvement on the surplus shortfall at a sharing game's equilibrium. The paper also obtains conditions for existence of (pure-strategy) equilibria and finds, in particular, that every finite game in which rewards are linearly related has an equilibrium.

In the rational expectations equilibrium of this paper, agents have private information and differing information partitions and therefore assign differing conditional distributions to asset payoffs and other economic variables relevant to their investment choices. Standard asset pricing models typically do not recognize the impact of these differing information partitions, and empirical tests based on these models thus measure asset riskiness in a way that may not be relevant to any of the agents' decisions. I show how this can lead to distorted estimates of investment risk and how it can make the equity premium appear difficult to explain.