Volume 8, Issue 1

We take a new look at the comparison between the Stackelberg equilibrium and the Cournot equilibrium. We show that, when the elasticity of the inverse market demand equals the curvature of the inverse market demand weighted by the Lerner Index, a generic Stackelberg leader sets the same quantity and earns the same profit as a generic Stackelberg follower. When the curvature of the inverse market demand equals the total number of firms in the industry, a coincidence among the quantities produced by a first mover, a second mover, and a generic firm facing Cournot competition occurs.

A principal, requiring a team to implement a project by proposing and jointly executing a technique, may benefit from choosing one with internal disharmony. When superior policy proposition by a member is rewarded with unitary executive control, the benefit of control is increasing in the degree of conflict. Hence, the presence of discord can raise incentives to take effort towards technique proposition by inducing competition for control, and thereby enhance average proposal quality. The principal may thus choose a fractious team when the losses from lower consensus in project execution are limited. These effects can be exacerbated in large teams, and lead to teamwork dominating individual production.

This paper examines the welfare effects of vertical integration by an "information gatekeeper" into the product market it serves. Both the integrated gatekeeper and competing firms in the product market earn higher profits, but social welfare declines.

We show that, even under incomplete markets, the equilibrium manifold identifies individual demands everywhere in their domains. Under partial observation of the manifold, we determine maximal subsets of the domains on which identification holds. For this, we assume conditions of smoothness, interiority and regularity. It is crucial that there be date-zero consumption. As a by-product, we develop a duality theory under incomplete markets.

We use a simple agency model to clarify and characterize the various avenues through which changes in the level of uncertainty impact the optimal strength of linear incentives. Instead of attempting to characterize different "types" of uncertainty, which has been the approach in the literature so far, we base our characterization on the link between uncertainty and the agent's action choice. We then use this characterization to provide conditions under which the relationship between uncertainty and incentives can be positive and relate it back to the existing models in the literature.

The effect that investment lags have on the uncertainty-investment relationship is studied by modifying the Bar-Ilan and Strange (1996) model to enable an analytical solution. The following results emerge: (i) If the time lag is sufficiently small, uncertainty affects investment negatively; (ii) A sufficiently large time lag gives rise to an inverse U-shape uncertainty-investment relationship; (iii) When such an inverse U-shape exists, the longer the time lag (or the larger the degree of profit convexity), the wider the range of a positive uncertainty-investment relationship.

We establish mathematical equivalence between independence of irrelevant alternatives and monotonicity with respect to first order stochastic dominance. This formal equivalence result between the two principles is obtained under two key conditions. Firstly, for all natural numbers m, each principle is defined on the domain of compound lotteries with compoundness level m. Secondly, the standard concept of reduction of compound lotteries applies.

Asymmetric information is widely supposed to impair the functioning of markets. We show that the presence of competition may invalidate this intuition. Consider a market in which principals compete for attracting heterogeneous agents by offering contracts. Suppose contracts are exclusive, and there are constant returns to trade. When the agents' types are publicly observed under mild conditions, competitive equilibria are efficient. Efficiency is also obtained when types are privately observed, provided that principals do not directly care about the agents' private information (the private value case). Thus hidden information only matters in competitive markets if it affects common values.

Anderson, Goeree and Ramer (1997) observe that although the Uniform consumer density is almost universally assumed in Hotelling style location games, it is more realistic to assume non-uniform distributions. Using Anderson et al.'s (1997) sufficient conditions for the existence of a unique pure strategy equilibrium, we extend the list of known distributions with characterised equilibria from two (Uniform and Triangular) to seven. Our extension includes the Normal and Logistic distributions which are commonly used in empirical research. We also analyse the effects of density choice on equilibrium outcomes. Holding the mean and dispersion of consumer tastes constant, we find that the Uniform distribution inflates differentiation effects.

The paper shows that market power may be an additional cause for the failure of PPP without making the usual assumption of segmentation of national markets. We construct an international multi-currency economy based on the strategic market game model with multiple trading posts, where, besides sellers, buyers have market power as well. Although arbitrage is costless, PPP may fail and exchange rates may be inconsistent at equilibrium due to agents' price effects in currency and commodity markets. We derive conditions on individual net trades and elasticities that result in PPP violation and exchange rate inconsistencies. A numerical example shows that when consistency fails, the ordering of prices is not well-defined. When the number of agents in the economy increases, PPP deviations and inconsistencies tend to zero, thus providing a strategic foundation of PPP theory. Furthermore, the size of PPP deviations is positively related to the number of currencies traded.

In this paper I apply stochastic stability to compare the effect on welfare of local information and global information when agents adopt imitative behavioral rules. Under global information, agents can potentially imitate anyone, while under local information, the sets of observable agents are choice-dependent. The evaluation of information in terms of welfare enhancement is ambiguous over finite time horizons, while in the long run global information is worse (better) in the presence of pure negative (positive) spillovers. However, when preferences also depend on the choice itself, further ambiguity emerges, generally making the comparison uncertain.

This paper explores how the costs of disclosing evidence affect the attainment of desirable outcomes in contractual relationships with complete information. Not only does evidence production cost influence the players' incentives to disclose evidence, it also affects their willingness to participate in a contractual relationship in which they may have to disclose evidence to convey information to a court about the state of the relationship. In some situations, evidence costs can interfere with the attainment of efficient outcomes, but in other situations evidence costs can help with attainment of efficient outcomes. A two-player production game in which investment influences the value of production and the players contract so as to shape investment incentives is used to illustrate these situations.

We reconsider the justifications of the R&D subsidies of Spencer and Brander (1983), by allowing firms to form a research joint venture (RJV) and license innovations. If governments offer unconditional subsidies, an RJV is formed and the strategic benefits of R&D subsidies vanish. Nevertheless, governments subsidize their domestic firms to enhance their bargaining position in the joint venture subgame. If governments offer subsidies conditional on forming resp. not forming an RJV, the game has multiple equilibria: one that restores the Spencer and Brander result, and another in which governments induce the formation of an RJV by a combination of conditional taxes and subsidies.

Comparative statics for all-pay auctions with two heterogeneous and privately informed bidders are analyzed. General results are provided for when one bidder becomes stochastically weaker. The comparative statics are fully characterized for truncations. Moreover, we show that expected revenue may increase when one bidder weakens. In the second part of the paper we consider a dynamic contest in which beliefs change endogenously: the first bidder may preempt the auction by paying a bribe. An all-pay auction is held if the bribe is not paid, in which case the second bidder revises his beliefs. With the option to bribe, expected payoff decreases for a set of types of at least one bidder, possibly the bidder ostensibly advantaged by the preemption option. However, the expected revenue and the ex ante payoff of both bidders may improve.

This paper investigates how additional ex post private information by the agent affects the equilibrium outcome of the monopolistic screening model. In general, the principal always weakly benefits when the agent receives additional private information after the contracting stage. Instead, both the agent's equilibrium payoffs and allocative efficiency may, due to the principal's concerns about information rents, increase or decrease. Moreover, we obtain the result that optimal contracts may involve lying off–the–equilibrium path and show that this exacerbates bunching in the monopolistic screening problem.

We consider bargaining between three firms that are all essential in creating a surplus. One of the firms is dominant in the sense that it ultimately decides whether the surplus will be created. The other firms have an incentive to get a large share of the pie for themselves, but leaving enough for the dominant firm that it finds it profitable to create the surplus. Hence, the smaller firms have preferences over who they take their share from. The bargaining takes place in sequence, and we identify optimal choice of bargaining framework for each firm. Conditions are presented under which a firm would prefer not to be represented at a stage in the negotiation process, and we show that the preferred order of bargaining for the dominant firm is also that which maximizes the total expected surplus from negotiation.

Simultaneous ascending auctions present agents with various strategic problems, depending on preference structure. As long as bids represent non-repudiable offers, submitting non-contingent bids to separate auctions entails an exposure problem: bidding to acquire a bundle risks the possibility of obtaining an undesired subset of the goods. With multiple goods (or units of a homogeneous good) bidders also need to account for their own effects on prices. Auction theory does not provide analytic solutions for optimal bidding strategies in the face of these problems. We present a new family of decision-theoretic bidding strategies that use probabilistic predictions of final prices: self-confirming distribution-prediction strategies. Bidding based on these is provably not optimal in general. But evidence using empirical game-theoretic methods we developed indicates the strategy is quite effective compared to other known methods when preferences exhibit complementarities. When preferences exhibit substitutability, simpler demand-reduction strategies address the own price effect problem more directly and perform better.

By revisiting the classic dirty-face problem we highlight the notion of `unawareness' (a simpler state space) and compare it with `impreciseness' (a coarser information partition). The outcomes are derived with various information structures. That allows us to 1) demonstrate a model of differing interpretations of public information using asymmetric awareness; 2) compare and contrast the impact of unawareness and impreciseness on learning; 3) analyze the value of awareness and the value of preciseness; and 4) demonstrate the effect of unawareness and impreciseness on information revelation with indirect aggregation.

The rate of cost pass-through exceeds 50% under strategic delegation of decision-making to managers with sales revenue contracts—regardless of the number of firms in the industry and demand curvature. This contrasts sharply with profit-maximization, for which cost pass-through can take on any positive value. The key intuition is that firms under delegation act as if they faced more rivals than they actually do, thus pushing cost pass-through towards 100%. Cost pass-through with market share contracts is similarly bounded below, and this note also generalizes existing results on equilibrium characterization for this case.

We analyze what can be inferred about a game's information structure solely from the probability distributions on action profiles generated during play; i.e., without reference to special behavioral assumptions or equilibrium concepts. Our analysis focuses on deriving payoff-independent conditions that must be met for one game form to be empirically distinguished from another. We define empirical equivalence and independence equivalence. The first describes when two game forms can never be distinguished based solely on the empirical distribution of player actions. As this turns out to be difficult to characterize, we introduce the latter, which describes two game forms that imply the same minimal sets of conditional independencies in every one of their empirical distributions. Our main contribution is to identify, for an arbitrary game form, the minimal set of conditional independencies that must arise in every one of its empirical distributions. We also introduce a new graphical device, the influence opportunity diagram of a game form which facilitates verifying independence equivalence, and hence provides a simple necessary condition for empirical equivalence.

A principal contracts with a productive agent whose production cost is private information and with an insurer who can insure the principal against variations in the payment to the agent. The insurer and the agent can collude in their responses to the principal's contract. Non-cooperative play of the principal's contract constitutes the outside option for the colluding parties. In this setup, we characterize the implementable outcomes for the principal. We then identify the optimal implementable outcome under the assumption that the principal faces a budget constraint. The optimal outcome provides the principal with "partial" insurance. For higher realizations of the production cost, the budget may not be exhausted even though the principal is not directly concerned with the unspent portion of the monetary funds.

In repeated games, equilibrium often requires that any deviation be punished in the continuation, regardless of whether it is beneficial to the other players. It seems against the nature of non-cooperative game theory for the other players to decide what to do based on what one player did, rather than on the well-being of themselves. We introduce a new solution concept called a forgiving-proof equilibrium that recommends continuing as if nothing had happened after a player deviates without harming the others. A folk theorem is established to characterize the set of forgiving-proof equilibrium payoffs when players are sufficiently patient. The concept of forgiving-proof equilibrium significantly reduces the set of equilibrium outcomes in many repeated games.

There is a wealth of research demonstrating that agents process information with the aid of categories. In this paper we study this phenomenon in two parts. First, we build a model of how experiences are sorted into categories and how categorization affects decision making. Second, in a series of results that partly characterize an optimal categorization, we show that specific biases emerge from categorization. For instance, types of experiences and objects that are less frequent in the population tend to be more coarsely categorized and lumped together. As a result, decision makers make less accurate predictions when confronted with such objects. This can result in discrimination against minority groups even when there is no malevolent taste for discrimination. However, such comparative statics are highly sensitive to the particular situation; optimal categorizations can change in surprising ways. For instance, increasing a group's population, holding all else constant, can lead a decision maker to make less accurate predictions about that group.

This paper addresses how a moderate evidence disclosure cost can be incorporated into mechanism-design analysis. The paper shows that in public-action settings with transferable utility one can restrict attention to a class of three-stage dynamic mechanisms. Under complete information with two or more players, a version of this type of mechanism can be used to eliminate evidence production in equilibrium. The paper also provides conditions on the evidence environment under which the class of mechanisms studied in Bull and Watson (2004) is equivalent to those considered here.

We introduce a new notion of connectivity, what we call weak connectivity, in a directed network where communication is one-way, and show that weak connectivity is equivalent to the usual concept of connectivity if the outdegree of each node is at most one, referred as the [DC] condition. Based on weak connectivity, we define an allocation rule in a directed network by applying the Shapley value type of consideration. We show that the allocation rule is the unique allocation rule satisfying component efficiency and equal bargaining power under the [DC] condition. If the [DC] condition does not hold, it fails to satisfy component efficiency, but can be shown to be the only allocation rule that satisfies equal bargaining power and quasi-component efficiency which is a weaker property.

We consider a setting in which several groups of individuals with common interests (``clubs") compete with each other for recognition by other individuals. Depending on the context, recognition may be expressed by these other individuals joining a club, or choosing one club to admire. Clubs compete by providing a public good. Competition between clubs increases the public good provision level, and a sufficiently strong competition effect may even lead to overprovision. The model thus limits the argument for subsidies to the private providers of public goods. We discuss implications of the model for open-source software projects, university fundraising and infrastructure competition between cities.

We consider the problem of when to deliver the contract payoff, in a continuous-time principal-agent setting, in which the agent's effort is unobservable. The principal can design contracts of a simple form that induce the agent to ask for the payoff at the time of the principal's choosing. The optimal time of payment depends on the agent's and the principal's outside options. We develop a theory for general utility functions, while with CARA utilities we are able to specify conditions under which the optimal payment time is not random. However, in general, the optimal payment time is typically random. One illustrative application is the case when the agent can be fired, after having been paid a severance payment, and then replaced by another agent. The methodology we use is the stochastic maximum principle and its link to Forward-Backward Stochastic Differential Equations.

We study a sequential trading financial market where there are gains from trade, that is, where informed traders have heterogeneous private values. We show that an informational cascade (i.e., a complete blockage of information) arises and prices fail to aggregate information dispersed among traders. During an informational cascade, all traders with the same preferences choose the same action, following the market (herding) or going against it (contrarianism). We also study financial contagion by extending our model to a two-asset economy. We show that informational cascades in one market can be generated by informational spillovers from the other. Such spillovers have pathological consequences, generating long-lasting misalignments between prices and fundamentals.

This paper extends the convergence result in Kalai and Lehrer (1993a, 1993b) to a class of games where players have a payoff function continuous for the product topology. Provided that 1) every player maximizes her expected payoff against her own beliefs, 2) every player updates her beliefs in a Bayesian manner, and 3) prior beliefs of other players' strategies have a grain of truth, we construct a Nash equilibrium such that, after some finite time, the equilibrium outcome of the above game is arbitrarily close to the constructed Nash equilibrium.

Consider a situation in which a principal commits to a mechanism first and then agents choose unobservable actions before their payoff-relevant types are realized. The agents' actions may affect not only their payoffs directly but also the distribution of their types as well. This paper extends Crémer and McLean's full surplus extraction theorem to such a setting. In this environment, it is shown that a principal may not succeed in extracting full surplus from agents when there are many actions to which the agents can deviate.However, it is also shown that a principal can extract full surplus generically given any approximately efficient (completely) mixed action profile. This is achieved by using a general mechanism where agents announce both their types and their realized actions. Therefore, with hidden actions, there is a big gap between exact full surplus extraction and approximate full surplus extraction.