Coordination and delay in global games

What is the effect of offering agents an option to delay their choices in a global coordination game? We address this question by considering a canonical binary action global game, and allowing players to delay their irreversible decisions. Those that delay have access to accurate private information at the second stage, but receive lower payoffs. We show that, as noise vanishes, as long as the benefit to taking the risky action early is greater than the benefit of taking the risky action late, the introduction of the option to delay reduces the incidence of coordination failure in equilibrium relative to the standard case where all agents must choose their actions at the same time. We outline the welfare implications of this finding, and probe the robustness of our results from a variety of angles.     

Large market games with demand uncertainty

We consider a market game with a continuum of consumers, where the measure of each type is stochastic. Nature selects the set of active consumers, who make bids and offers on ?−1 spot market trading posts. Existence of type-symmetric Nash equilibrium is proven. When facing price uncertainty, best responses are unique, and a Nash equilibrium to the sell-all game is typically not a Nash equilibrium to the original game. Under plausible circumstances, consumers strictly prefer to be on one side of the market.     

Cooperation in Stochastic OLG games

This paper builds on Cremer's (Quart. J. Econ. 101 (1986) 33) seminal analysis which shows that (almost) complete cooperation can be achieved as an equilibrium in a game played by overlapping generations of players if the institution in which players cooperate is infinitely lived.We analyze a similar model in which the costs of cooperation are subject to random shocks. Even if these random shocks are very small, the range of parameters for which cooperation can be sustained is decreased considerably in comparison to the deterministic case. Furthermore, we show how the efficient outcome can be approximated if the level of cooperation can be varied continuously and the cooperation technology has decreasing or constant returns to scale, while this is not possible in the case of increasing returns to scale.     

Noise-independent selection in multidimensional global games

This paper examines many-player many-action global games with multidimensional state parameters. It establishes that the notion of noise-independent selection introduced by Frankel, Morris and Pauzner [D. Frankel, S. Morris, A. Pauzner, Equilibrium selection in global games with strategic complementarities, J. Econ. Theory 108 (2003) 1–44] for one-dimensional global games is robust when the setting is extended to the one proposed by Carlsson and Van Damme [H. Carlsson, E. Van Damme, Global games and Equilibrium selection, Econometrica 61 (1993) 989–1018]. More precisely, our main result states that if an action profile of some complete information game is noise-independently selected in one-dimensional global games, then it is also noise-independently selected in all multidimensional global games.     

Games of social interactions with local and global externalities

In this paper we present a result on the existence of pure strategies Nash equilibrium which covers a large class of games with local and global social interactions. The result highlights common features of well-known games analyzed in the literature.     

Equilibrium selection in global games with strategic complementarities

We study games with strategic complementarities, arbitrary numbers of players and actions, and slightly noisy payoff signals. We prove limit uniqueness: as the signal noise vanishes, the game has a unique strategy profile that survives iterative dominance. This generalizes a result of Carlsson and van Damme (Econometrica 61 (1993) 989-1018) for two-player, two-action games. The surviving profile, however, may depend on fine details of the structure of the noise. We provide sufficient conditions on payoffs for there to be noise-independent selection.     

Learning to play Bayesian games

This paper discusses the implications of learning theory for the analysis of games with a move by Nature. One goal is to illuminate the issues that arise when modeling situations where players are learning about the distribution of Nature's move as well as learning about the opponents' strategies. A second goal is to argue that quite restrictive assumptions are necessary to justify the concept of Nash equilibrium without a common prior as a steady state of a learning process.     

Credible assignments can improve efficiency in laboratory public goods games

This paper reports an experiment investigating how assignments improve economic efficiency in a modified version of the standard voluntary-contributions mechanism. The experiment uses a non-binding message that makes common information assignments in the repeated game. A credible assignment is one actually followed by the participants. It turns out to be difficult to credibly assign the symmetric efficient outcome in four person cohorts, but we did discover one assignment that was credible in the last match of the evolutionary repeated game.     

Trembling-hand myopia and trembling-hand perfection

In 1975 Selten introduced trembling-hand perfection, however it was implicitly assumed that specific values of rationality imperfections are common knowledge. Relaxing this assumption, we develop the notion of trembling-hand myopia, and completely characterize equilibria which are robust in this setting.     

A note on cheap talk and burned money

Austen-Smith and Banks [Cheap talk and burned money, J. Econ. Theory 91(1) (2000) 1-16] study how money burning can expand the set of pure cheap talk equilibria of Crawford and Sobel [Strategic information transmission, Econometrica 50(6) (1982) 1431-1451]. I identify an error in the main Theorem of Austen-Smith and Banks, and provide a variant that preserves some of the important implications. I also prove that cheap talk can be influential with money burning if and only if it can be influential without money burning. This strengthens a result of Austen-Smith and Banks, but uncovers other errors in their analysis. Finally, an open conjecture of theirs is proved correct.     

Unique equilibrium in rent-seeking contests with a continuum of types

It is shown that rent-seeking contests with continuous and independent type distributions possess a unique pure-strategy Nash equilibrium.     

A two-person game of information transmission

We consider a statistical decision problem faced by a two player organization whose members may not agree on outcome evaluations and prior probabilities. One player is specialized in gathering information and transmitting it to the other, who takes the decision. This process is modeled as a game. Qualitative properties of the equilibria are analyzed. The impact of improving the quality of available information on the equilibrium welfares of the two individuals is studied. Better information generally may not improve welfare. We give conditions under which it will.     

Uniform selection in global games

This paper brings together results which are required in order to extend the global games approach to settings where the game structure is endogenous. More precisely, it shows that the selection argument of Carlsson and van Damme [Global games and equilibrium selection, Econometrica 61(5) (1993) 989-1018] holds uniformly over appropriately controlled families of games. Those results also give proper justification for the inversion of limits which is often implicit in applied work taking comparative statics on the selected risk-dominant equilibrium.     

Delays and equilibria with large and small information in social learning

The general model of social learning with irreversible investment and endogenous timing is analyzed for any distribution of private informations. Strategic complementarities and multiple equilibria appear which are generated solely by information externalities. Different equilibria generate strikingly different amounts of information. The impacts of various assumptions (bounded beliefs, large number of agents, discrete time and short periods) are examined carefully. The properties are robust to the introduction of observation noise with a continuum of agents.     

After you—endogenous sequencing in voluntary contribution games

We examine contributions to a public good when some donors do not know the true value of the good. If donors in such an environment determine the sequence of moves, two contribution orders may arise as equilibria. Either the uninformed and informed donors contribute simultaneously or the informed contribute prior to the uninformed. Sequential moves result in a larger provision of the public good, because the follower mimics the action of the leader, and in accounting for this response the leader chooses to contribute when it is efficient to do so. An experimental investigation of the game shows that the donors predominantly choose to contribute sequentially, and that the resulting contributions are larger than those of the simultaneous-move game. Although the gain from sequential moves is smaller when the sequence is set exogenously, our results suggest that the involved parties would benefit from having sequential moves imposed upon them.     

Decision-making in competitive framings—Strategic behavior of chess players in mini-ultimatum game chess puzzles

We introduce a competitive framing in the mini-ultimatum game utilizing chess puzzles. Therein, our chess playing participants accept low offers significantly more often compared to a neutral framing. We conclude that in familiar competitive surroundings egoistic behavior is more acceptable.     

Risk-sharing and crises. Global games of regime change with endogenous wealth

I add heterogeneous agents and risk-sharing opportunities to a global game of regime change. The novel insight is that when there is a risk-sharing motive, fundamentals drive not only individual behavior, but also select which individuals are more relevant for the likelihood of a crisis because of endogenous shifts in wealth. If attacking is relatively safe, attack behavior in the global game and trade in state-contingent assets feed back into each other. This feedback implies that multiple equilibria may exist even if signal noise becomes arbitrarily small. In addition, heterogeneity in risk-aversion within the population amplifies the influence of the state of the economy on the probability of a crisis.     

Balanced Bayesian mechanisms

In the transferable utility case, a number of authors have identified conditions on beliefs that guarantee the existence of Bayesian incentive compatible mechanisms with balanced transfers. We present a new, easy to interpret, condition and we show that it is (strictly) more general than all the other conditions found in the literature. We also study conditions guaranteeing the Bayesian implementability of all social decision rules with balanced budget mechanisms.     

Cheap talk in games with incomplete information

The paper studies Bayesian games which are extended by adding pre-play communication. Let Γ be a Bayesian game with full support and with three or more players. The main result is that if players can send private messages to each other and make public announcements then every communication equilibrium outcome, q, that is rational (i.e., involves probabilities that are rational numbers) can be implemented in a sequential equilibrium of a cheap talk extension of Γ, provided that the following condition is satisfied: There exists a Bayesian Nash equilibrium s in Γ such that for each type t_i of each player i the expected payoff of t_i in q is larger than the expected payoff of t_i in s.