Volume 12, Issue 1

We study seller cheap talk problem in a modified almost common value auction, where there are potential entrants who need to pay entry costs for entering the auction. In almost common value auctions, a seller suffers great revenue losses due to the aggravated winner's curse problem. In our modified model, the inside bidders are more sensitive to the signals sent by the seller, and by revealing the information about the object valuation, the seller faces the trade-off between the benefit of increased competition and that of higher bids by weak inside bidders. For instance, a low message will attract the potential entrants into the auction, as a result of greater winning opportunity, and a high message will encourage the weak since bidders to bid more aggressively, as a result of increased valuation. Under quite plausible conditions, there exists an informative equilibrium in this cheap talk game, which will either increase the expected revenue of the auction, or the efficiency of final allocation.

It is well known that non-renegotiable contracts with third parties may have an effect on the outcome of a strategic interaction and thus serve as a commitment device. We address this issue when contracts are renegotiable. More precisely, we analyze the equilibrium outcomes of two-stage games with renegotiation-proof third-party contracts in relation to the equilibrium outcomes of the same game without contracts. We assume that one of the parties in the contractual relationship is unable to observe everything that happens in the game when played by the other party. We first show that when contracts are non-renegotiable, the set of equilibrium outcomes of the game with contracts is restricted to a subset of Nash equilibrium outcomes of the original game. Introducing renegotiation, in general, imposes further constraints and in some games implies that only subgame perfect equilibrium outcomes of the original game can be supported. However, there is a large class of games in which non-subgame perfect equilibrium outcomes can also be supported, and hence, third-party contracts still have strategic implications even when they are renegotiable.

In a model of decision making over sets of alternatives, we consider an agent who conceives of the different utilities she will receive (depending on the state of mind she is in, her subjective state) when she finally makes a choice from the set. Her uncertainty is described by multiple beliefs (or measures) over the state space. She is pessimistic about the true beliefs, and would like to hedge her bets. This results in her having a preference for uniformity of payoffs across the various subjective states. We present a utility representation for such agents and show that our representation provides a natural measure of the agent's desire for uniformity of payoffs in the subjective states. We also show that concerns for uniformity are orthogonal to concerns about flexibility or commitment. We achieve this by relaxing the Independence axiom as applied to our environment. However, this weakening of Independence means that in settings with temptation, we can no longer ensure the existence of a unique normative ranking.

Using laboratory experiments, we compare the performance of first-price and second-price auctions when two stochastically equivalent objects are auctioned sequentially and the winner of the first auction receives a positive synergy in the second auction. According to the risk-neutral subgame perfect Nash equilibrium, the second-price auction provides more efficiency and a higher revenue to the seller, but a lower ex ante expected payoff to the bidders. Our experimental data indicate precisely the opposite results for format comparisons: the first-price auction gives rise to larger levels of efficiency and revenue, but lower payoffs to the bidders. Despite the lower payoff, the likelihood of an ex post loss is also smaller under the first-price auction. Our results therefore support the common use of the first-price auction in governmental and business-to-business procurements.

An agent, who cares about signaling his ability, chooses among different projects that generate observable outcomes. The agent's information about which project delivers a good outcome depends on both his ability and his effort. This paper examines how the agent's incentives for effort change depending on whether or not the agent's project choice is observed. If this choice is publicly observed, the agent's project choice is distorted towards particular types of projects. When the outcomes of these advantaged projects are particularly sensitive to the agent's information, such transparency boosts the agent's information-gathering incentives. However, when public observation of project choice leads the agent to choose information-insensitive projects, then such transparency dampens incentives. This provides a more nuanced view of the implications of action transparency in the literature on career concerns for experts.

In many contracting settings incentives are provided not only through transfers but also through performance reports to prospective employers. This paper studies a principal-agent model of this kind, in which the principal sends a non-verifiable report of output to a competitive labor market interested in the agent's ability. It is assumed that the principal and agent write an enforceable contract over both payments and reports as a function of output, and that the contract terms they agree to cannot be observed by the market. When contracts are unrestricted, reports cannot affect the agent's future wage in equilibrium, because the agent will always pay the principal to give a good report. Under limited liability, reports can affect future wages, but only by designating output as "good" or "bad." This informative performance reporting benefits the principal, and may more than make up for the costs imposed by limited liability. The possibilities that the market may have some direct information about output, that the principal may have additional information about the agent's ability, and that the principal may have psychological or reputational costs of misreporting output are also considered.

We exhibit a new equilibrium of the classic Blotto game in which players allocate one unit of resources among three coordinates and try to defeat their opponent in two out of three. It is well known that a mixed strategy will be an equilibrium strategy if the marginal distribution on each coordinate is U[0,(2/3)]. All classic examples of such distributions have two-dimensional support. Here we exhibit a distribution which has one-dimensional support and is simpler to describe than previous examples. The construction generalizes to give one-dimensional distributions with the same property in higher-dimensional simplices as well.As our second note, we give some results on the equilibrium payoffs when the game is modified so that players have unequal budgets. Our results suggest a criterion for equilibrium selection in the original symmetric game, in terms of robustness with respect to a small asymmetry in resources.

The paper introduces a new allocation game, related to Blotto games: each tennis coach assigns his four different skilled players to four positions, and then each team plays all other teams in the tournament. The winning team is the one with the highest total score.The set of equilibria is characterized and experimental behavior in variants of the game is analyzed in light of an adapted level-k model which is based on an appealing specification of the starting point (Level-0). The results exhibit a systematic pattern- a majority of the subjects used a small number of strategies. However, although level-k thinking is naturally specified in this context, only a limited use of (low) level-k thinking was found. These findings differ from those obtained in previous studies, which found high frequencies of level-k reasoning among subjects in various games. Thus, the results illuminate some bounds of the level-k approach.

In this paper we consider a duopoly model of multidimensional vertical product differentiation where product features are discrete and consumers' tastes are described by a joint density function that belongs to the class of Elliptically Contoured Distributions. We prove that in any equilibrium one firm always includes all characteristics in the product. Moreover, when types have perfect positive correlation the unique equilibrium involves maximum differentiation. More importantly, the main result states that the other firm's equilibrium level of differentiation is determined by the correlation among types.

This paper considers an investor who, at a cost, can acquire a signal about an entrepreneurial project's payoff. The problem for this investor is that uninformed investors can compete to provide funding and the informed investor's contract offer conveys information to the entrepreneur about the project's likely payoffs, affecting the attractiveness of the entrepreneur's uninformed funding alternatives. I determine how the investor's choices of signal quality and contracting terms are affected by project primitives. I prove that equilibrium expected payoffs in this signaling game are unique and that equilibrium strategies solve simple optimal contracting problems, showing that informed investors can use equity, and that uninformed investors compete with simple debt. Finally, I show that introducing the possibility of commitment by the informed investor alters the structure of the game, but not equilibrium payoffs.

We extend Dekel and Wolinsky's (2003) result on private-value first price auctions by providing different sufficient conditions under which each player has a unique rationalizable bid conditional on her value. Unlike Dekel and Wolinsky's, our result does not necessarily require a large number of players. If values are independently distributed, (i) our conditions are weaker than Dekel and Wolinsky's, and (ii) our conditions require a large number of players only if the distributions on values has a low reverse hazard rate for some value. Our result holds for the cases where players' utility functions are concave or values are not identically distributed.

This paper studies the role of commitment in the design of enforcement mechanisms when enforcement can remedy harm from non-compliance. We consider a game between an enforcement authority ("enforcer") and an offender in which either the enforcer or the offender may act as a Stackelberg leader. The enforcer must choose whether to move first by committing to an enforcement strategy--thereby directly affecting the level of non-compliance; or rather let the offender make the first move--thereby calibrating the level of enforcement to the actual level of non-compliance. We show that the value of commitment to the enforcer depends on each player's responsiveness to a change in the other player's strategy choice. Commitment to an enforcement strategy is thus not always in the enforcer's interest.

People's past decisions often play a significant role in shaping their future preferences. Based on this premise, we propose a model of endogenously changing preferences in an intertemporal environment. The two types of agents are distinguished by their self-knowledge of the dynamically inconsistent preferences. In particular, we study the dynamic contract design problem of a monopolistic principal in this setup. Commitment contracts and spot contracts are contrasted. When types are known to the principal, commitment contracts are superior to spot arrangements. When types are unobservable, we arrive at several unconventional results. First, the first best outcome can still be achieved in the case of commitment contracts. Second, informational externality may extend in both directions when the first best spot contracts are not incentive compatible. Lastly, in the second best spot contracts, informational rent may accrue to both types of agents.

This paper considers an economy populated by a sequence of generations who decide over their consumption and investment in human capital of their immediate descendants. In such a framework, we first identify the impact of strategic interactions between consecutive generations on the time path of human capital accumulation. To this end, we characterize the decentralized Markov stationary Nash equilibrium (MSNE) and derive the sufficient conditions for its existence and uniqueness. We then provide sufficient conditions under which human capital accumulation is unambiguously (pointwise) lower in the ``strategic'' equilibrium than under the optimal dynastic policy, and discuss an example where this ordering does not hold. Secondly, we also run a numerical sensitivity analysis to assess the magnitude of discrepancies between the two analyzed cases and discuss the potential implications of overestimation of the human capital role if intergenerational interactions are not accounted for.

We investigate a model in which one seller and one buyer trade in each of two periods. The buyer has demand for one unit of a non-durable object per period. The buyer's reservation value for the good is private information and is the same in both periods. The seller commits to prices in each of two periods. Prices in the second period may depend on the buyer's first-period behavior. Unlike the equal discount factor case studied in earlier papers, we show that when the seller is more patient than the buyer, second-period prices increase after a purchase. In particular, the optimal dynamic pricing scheme is not a repetition of the optimal static pricing scheme.

This paper studies altruistic behavior in a model of local interaction. Individuals live on a circle and choose whether to altruistically provide a local public good. Choices are based on imitation of successful neighbors and experimentation. The public good is assumed to be less local than imitation. In the absence of experimentation altruism can prevail and coexist with egoism as long as the public good is non-global. With experimentation altruism persists in the long run only if the population is large relative to the reach of the public good.

This paper develops and explores signaling in the market for education based on imperfectly observed heterogeneity in the returns to education rather than heterogeneity in costs. Workers of heterogeneous abilities face the same costs of education, yet the productivity gain from education is higher for more able workers, and employers' observations of productivity are noisy. The paper presents the necessary and sufficient condition replacing the single crossing property in this context, proves that no separating equilibrium exists, and analyzes the mixed strategy equilibrium to produce some new results due to the presence of strategic complementarities.

We define an arbitration problem as the triplet of a bargaining set and the offers submitted by two players. We characterize the solution to a class of arbitration problems using the axiomatic approach. The axioms we impose on the arbitration solution are "Symmetry in Offers,'' "Invariance'' and "Pareto Optimality.'' The key axiom, "Symmetry in Offers,'' requires that whenever players' offers are symmetric, the arbitrated outcome should also be symmetric. We find that there exists a unique arbitration solution, called the symmetric arbitration solution, that satisfies all three axioms. We then analyze a simultaneous-offer game and an alternating-offer game. In both games, the symmetric arbitration solution is used to decide the outcome whenever players cannot reach agreement by themselves. We find that in both games, if the discount factor of players is close to 1, then the unique subgame perfect equilibrium outcome coincides with the Kalai-Smorodinsky solution outcome.

This paper studies the interactions between democratization and the emergence of rule of law. We propose a model in which heterogeneous individuals can make costly investments to protect their income against expropriation. The public enforcement of property rights is chosen by the enfranchised population whose composition depends on the political regime in place. We characterize the politico-economic equilibria in terms of property rights protection and political regime, and study the role of the different scenarios of democratization. The results suggest: (i) unequal control of natural resources is a central structural determinant of the democratization scenario; (ii) democratic transitions under conflict may lead to failed democracies with poor rule of law; (iii) that democratic transitions supported by a large consensus may serve as a coordination device thereby leading to better protection of property rights and more stable polities.

We consider a decision maker who enjoys choosing from a varied set of alternatives. Building on behavioral evidence, we propose testable axioms which characterize preference for variety and provide a representation theorem. We go on to illustrate the potential effects of preference for variety in a model of retailing. Consumer welfare may be decreasing in the competitiveness of the retailing sector as competition eliminates the scope for retailers to offer variety. Mainstream consumers with a preference for variety and consumers with eccentric tastes enjoy a symbiotic relationship. Competition over mainstream consumers makes retailers offer more exotic goods, while eccentric consumers subsidize their carrying costs.

We introduce a general framework for formalizing and analyzing the problem faced by a Decision Maker (DM) working under information-theoretic constraints on their observational ability. The random utility model and the "hedonic utility" model of Netzer and Robson (NR) are special cases of this framework. We begin by applying information theory to our framework to derive general results concerning the expected regret of DM under observational limitations. We then turn our attention to the effects of observational limitations on choice behavior (rather than their effects on the regret values induced by that behavior). We focus on the special case of NR. First we derive two postulates assumed by NR. We then provide a simple derivation of the result of NR that a particular hedonic utility function satisfies certain optimality principles. Next we extend NR to allow a countable, rather than uncountable, set of states of the world. In particular we show how to use dynamic programming to solve for the optimal preference order of DM in this extension. We also extend NR by considering the case where more than two options are presented to DM. In particular, we show that the results of NR change in such a case, implying that the number of options being presented is a crucial aspect of choice problems.

We prove strict concavity of the value function for liquidity constrained dynamic accumulation models without adopting at least one of the following restrictive assumptions: zero response of productive effort, bounded marginal value of accumulated balances, or strictly convex cost of holding accumulated balances. Thus we extend well known theoretical results to more general models of saving with liquidity constraints and of commodity storage with non-negativity constraints on stocks. Our results provide a foundation for estimation of a homogeneous markovian process for consumption in models of saving, or for price in commodity storage models, under more realistic assumptions.

This paper studies frequent monitoring in an infinitely repeated game with imperfect public information and discounting, where players observe the state of a continuous time Brownian process at moments in time of length Δ. It shows that a limit folk theorem can be achieved with imperfect public monitoring when players monitor each other at the highest frequency, i.e., Δ↓0. The approach assumes that the expected joint output depends exclusively on the action profile simultaneously and privately decided by the players at the beginning of each period of the game, but not on Δ. The strong decreasing effect on the expected immediate gains from deviation when the interval between actions shrinks, and the associated increase precision of the public signals, make the result possible in the limit.

In the problem of assigning indivisible goods and monetary transfers, we characterize welfare-egalitarian mechanisms (that are decision-efficient and incentive compatible) with an axiom of solidarity under preference changes and a fair ranking axiom of order preservation. This result is in line with characterizations of egalitarian rules with solidarity in other economic models. We also show that we can replace order-preservation with egalitarian-equivalence or no-envy (on the subadditive domain) and still characterize the welfare-egalitarian class. However, if we weaken order preservation to symmetry, mechanisms that are not welfare-egalitarian exist. We also study upper bounds on deficit and welfare lower bounds that characterize subclasses of the welfare-egalitarian class.

In variants of the Electronic Mail Game (Rubinstein, 1989) where two or more players communicate via multiple channels, the multiple channels can facilitate collective action via redundancy, the sending of the same message along multiple paths or else repeatedly along the same path (Chwe, 1995 and De Jaegher, 2011). This paper offers another explanation for how multiple channels may permit collective action: parties may be able to coordinate their actions when messages’ arrivals at their destinations are sufficiently correlated events. Correlation serves to fill in information gaps that arise when players are uncertain of the source of message failure, effectively strengthening messages from one player. This asymmetry in message strength in turn permits cutoff equilibria, where players take action after receiving a minimum number of confirmations.

In an environment of independent private values, we show that k-price auctions (k>2) with a large number of bidders are dominance solvable in two steps. Specifically, if bidders are rational and are certain that their opponents are rational (but without requiring deeper levels of reasoning), then bids converge to true valuations as the economy gets larger. Our model allows for heterogeneity in bidders' attitudes to risk and in the distributions from which valuations are drawn.

This paper extends the analysis of liberal principles in social choice recently proposed by Mariotti and Veneziani (2009a) to infinitely-lived societies. First, some novel characterisations of inegalitarian leximax social welfare relations are derived based on the Individual Benefit Principle (IBP), which incorporates a liberal, non-interfering view of society. This is surprising because the IBP does not explicitly incorporate any preference for inequality, nor does it assign priority to well-off members of society. Second, some impossibility results are derived that highlight a general tension between standard fairness and efficiency axioms in social choice, and a liberal Principle of Non-Interference that generalises IBP.

In this paper we study learning procedures when counterfactuals (payoffs of not chosen actions) are not observed. The decision maker reasons in two steps: First, she updates her propensities for choosing each action after every payoff experience, where propensities can be interpreted as preferences. Then, she transforms these propensities into choice probabilities. We introduce a set of axioms on how propensities are updated and on how these propensities are translated into choices and study the decision marker's behavior when such axioms are in place. Our characterization includes the linear reinforcement learning rule from Roth and Erev (1995).

We establish that a novel notion of similarity with endowments by Shitovitz and Spiegel (1998) amounts to severe functional form restrictions, and these restrictions on utility functions can be determined by functional equation methods. The resulting functional forms are related to the familiar Cobb-Douglas and quasi-linear forms, as well as the classical result of Bergstrom and Cornes (1983) on the independence of allocative efficiency from distribution in the theory of public goods.

While the significance of economies of scale in outsourcing has been well-documented, the consequences of outsourcing on firms' R&D efforts, when outsourcing is driven by scale economies, remains unexplored. We investigate a simple model where downstream competitors outsource to a common upstream supplier out of their incentive to better exploit scale economies. We find that the efficiency gain of outsourcing in virtue of economies of scale helps to internalize R&D spillovers, which tends to enhance outsourcing firms' R&D incentives. On the other hand, outsourcing also mitigates downstream competition, which imposes an ambiguous impact on outsourcing firms' R&D incentives. The aggregate effect is that outsourcing enhances R&D investments only when R&D spillovers are sufficiently large, or when upstream economies of scale are sufficiently small.

The weak sequential core is a solution concept to coalition formation under uncertainty when only non-binding agreements can be formed ex ante. Here the case where any deviation from an allocation must be robust to communication both within, and between, coalitions at the ex ante stage is considered. The communication-proof weak sequential core is advanced as an alternative solution concept. Examples, including a production economy, are used to demonstrate the differences between the solutions. Finally, sufficient conditions for the non-emptiness of the communication-proof weak sequential core are provided.

The asymmetry of single-peaked preferences has scarcely been incorporated as an assumption in economic models. We analyze how to deal with asymmetric single-peaked preferences in a tractable way. We define natural types of asymmetries, provide the tools to compare degrees of asymmetry, and propose concrete utility functions that represent different directions and degrees of asymmetry. As an application, we provide a representative voter theorem which establishes the heterogeneity in degrees of asymmetry across agents that is compatible with the median being the representative voter.

It is well known that bargaining with incomplete information incurs a substantial amount of inefficiency. We consider a bargaining procedure in which the seller makes a "take-it-or-leave-it" offer to a buyer. An initial stage in which the buyer is permitted to convey information to the seller is introduced into this framework. The decision regarding what information will be conveyed is made before the buyer knows his exact valuation. We study the type of information the buyer would be willing to transmit to the seller. The analysis determines that buyers with low valuations, in effect, reveal their valuations whereas buyers with high valuations conceal them. Communication between buyer and seller before the bargaining process begins improves both the overall efficiency of the process as well as the welfare of both buyer and seller.