Recombinant estimation for normal-form games,with applications to auctions and bargaining

When analyzing economic games, researchers frequently estimate quantities describing group outcomes, such as the expected revenue in an auction. For such applications, we propose an improved statistical estimation technique called “recombinant estimation.” The technique takes observations of players' strategies and recombines them to compute all possible group outcomes that could have resulted from different player combinations. In applications to an auction and a bargaining game, the improved efficiency of our estimator is equivalent to increasing the sample size between 25 and 200%. We discuss how to design experiments in order to utilize recombinant estimation. We also discuss practical computational issues, and provide software for computing estimates and standard errors.     

Coalition formation in general apex games under monotonic power indices

An apex game consists of one apex player and a set of minor players. We identify two key properties of apex games and use them to introduce the class of general apex games. We derive players' preferences over winning coalitions by applying strongly monotonic power indices on such a game and all its subgames and investigate whether there are core stable coalitions in the induced hedonic coalition formation game. Besides several general results, in particular, we develop conditions on the game for the Shapley–Shubik index, the Banzhaf index, and the normalized Banzhaf index.     

Information can wreck cooperation: A counterpoint to Kandori (1992)

We propose a simple model of repeated games with private monitoring and time-varying information structures. We then obtain an example demonstrating that the set of achievable equilibrium payoffs may shrink when players' information regarding opponents' information structures is increased.     

Continuous time limits of repeated games with imperfect public monitoring

In a repeated game with imperfect public information, the set of equilibria depends on the way that the distribution of public signals varies with the players' actions. Recent research has focused on the case of “frequent monitoring,” where the time interval between periods becomes small. Here we study a simple example of a commitment game with a long-run and short-run player in order to examine different specifications of how the signal distribution depends upon period length. We give a simple criterion for the existence of efficient equilibrium, and show that the efficiency of the equilibria that can be supported depends in an important way on the effect of the player's actions on the variance of the signals, and whether extreme values of the signals are “bad news” of “cheating” behavior, or “good news” of “cooperative” behavior.     

Ex ante contracting with endogenously determined communication plans

Summary. In this paper we introduce a new model of ex ante contracting for economies with asymmetric information to examine endogenously determined communication plans for information sharing in the interim stage. In contrast to the models used in previous research, in the present model agents negotiate not only on a contract of state contingent allocations but also on a communication plan, a set of rules describing how agents will reveal part of their private information at the interim stage to execute the trade contracts. We prove a result about the nested structure of the set of allocations implementable by various communication plans and establish the existence of core strategies for this cooperative game under various regularity conditions. Received: 4 March 1998; revised version: 17 September 1999     

SOCIAL INTERACTIONS IN LARGE NETWORKS: A GAME THEORETIC APPROACH

This article studies estimation of social interactions in a large network game, where all observations come from one single equilibrium of a network game with asymmetric information. Simple assumptions about the structure are made to establish the existence and uniqueness of the equilibrium. I show that the equilibrium strategies satisfy a network decaying dependence condition requiring that dependence between two players' decisions decay with their network distance, which serves as the basis for my statistical inference. Moreover, I establish identification and propose a computationally feasible and efficient estimation method, which is illustrated by an empirical application of college attendance.     

Edgar Allan Poe's riddle: Framing effects in repeated matching pennies games

Framing effects have a significant influence on the finitely repeated matching pennies game. The combination of being labelled “a guesser,” and having the objective of matching the opponent's action, appears to be advantageous. We find that being a player who aims to match the opponent's action is advantageous irrespective of whether the player moves first or second. We examine alternative explanations for our results and relate them to Edgar Allan Poe's “The Purloined Letter.” We propose a behavioral model which generates the observed asymmetry in the players' performance.     

Cycles of Learning in the Centipede Game

This paper studies the evolutionary properties of the Centipede Game. For this game, the use of backward induction as a model of rational behavior has been consistently challenged by the experimental evidence. Our claim is that backward induction can still accurately predict the players' behavior, provided that they are given time enough to appreciate the strategic environment in which they operate. We support this claim by proving convergence to the backward induction solution for all continuous-time monotonic selection dynamics. However, we also show that this solution is intrinsically unstable, and how this instability is positively related to the length of the game. Journal of Economic Literature Classification Numbers: C72, C79.     

Optimal contracting with altruism and reciprocity

Motivated by the recent experimental evidence on altruistic behavior, we study a simple principal–agent model where each player cares about other players' utility, and may reciprocate their attitude towards him. We show that, relative to the selfish benchmark, efficiency improves when players are altruistic. Nevertheless, in contrast to what may be expected, an increase in the degree of the agent's altruism as well as a more reciprocal behavior by players has ambiguous effects on efficiency. We also consider the effects of the presence of spiteful players and discuss how monetary transfers between players depend on their degrees of altruism and spitefulness.     

Speculative Attacks with Multiple Sources of Public Information*

We propose a speculative attack model in which agents receive multiple public signals. Diverse pieces of public information can be taken into account differently by different players and are likely to lead to different appreciations ex post. This process defines players' expected private values of a successful attack. The main result shows that equilibrium uniqueness depends on two conditions: (i) signals are sufficiently dispersed and (ii) private beliefs about signals' relative precision differ sufficiently. We derive some implications for information dissemination policy. Transparency in this context is multidimensional: it concerns the publicity of announcements, the number of signals disclosed and their precision.     

An Experiment to Evaluate Bayesian Learning of Nash Equilibrium Play

We report on an experiment designed to evaluate the empirical implications of Jordan's model of Bayesian learning in games of incomplete information. A finite example is constructed in which the model generates unique predictions of subjects' choices in nearly all periods. When the “true” game defined by players' private information was one with a unique equilibrium in pure strategies, the experimental subjects' play converged to the equilibrium, as Jordan's theory predicts, even when the subjects had not attained complete information about one another. But when there were two pure strategy equilibria, the theory's predictions were not consistent with observed behavior. Journal of Economic Literature Classification numbers: D83, C72, C92.     

Game Theory via Revealed Preferences

We investigate equilibrium notions in game theory from the revealed preference approach. For extensive game forms with complete information, we derive a set of independent necessary and sufficient conditions for the observed outcomes to be rationalized by subgame-perfect Nash equilibrium. Journal of Economic Literature Classification Numbers: C72, C92.     

How Much Common Belief Is Necessary for a Convention?

We study Bayesian coordination games in which players choose actions conditional on the realization of their respective signals. Due to differential information, the players do not have common knowledge that a particular game is being played. However, they do have common beliefs with specified probabilities concerning their environment. In our framework, any equilibrium set of rules must be simple enough so that the actions of all players are common belief with probability 1 at every state. Common belief with probability close to 1 will not do.Journal of Economic LiteratureClassification Numbers: C72, D82.     

Electricity market mergers with endogenous forward contracting

We analyze the effects of electricity market mergers in an environment where firms endogenously choose their level of forward contracts prior to competing in the wholesale market. We apply our model to Alberta’s wholesale electricity market. Firms have an incentive to reduce their forward contract coverage in the more concentrated post-merger equilibrium. We demonstrate that endogenous forward contracting magnifies the price increasing impacts of mergers, resulting in larger reductions in consumer surplus. Current market screening procedures used to analyze electricity mergers consider firms’ pre-existing forward commitments. We illustrate that ignoring the endogenous nature of firms’ forward commitments can yield biased conclusions regarding the impacts of market structure changes such as mergers. In particular, we show that the price effects of mergers can be largely underestimated when forward contract quantities are held at pre-merger levels. Whether the profits of the merged firm are greater with fixed or endogenous forward quantities is ambiguous.     

JUMPING THE CURSE: EARLY CONTRACTING WITH PRIVATE INFORMATION IN UNIVERSITY ADMISSIONS*

This article introduces a new model of early contracting. Employers who have private information about the applicant's ability worry that applicants who accept their offer are precisely those who were not offered other jobs. To avoid this winner's curse, employers anticipate the time of contracting. The model is developed in the context of university admissions, and is shown to be consistent with several stylized facts in that “market.” We show that, in contrast to received wisdom, allocative efficiency may be improved by the presence of early contracting.     

Incorporating rigidity and commitment in the timing structure of macroeconomic games

This paper proposes a novel framework that generalizes the timing structure of games. Building on alternating move games and models of rational inattention, the players' actions may be rigid, i.e., infrequent. This rigidity in the timing of moves makes the game more dynamic and asynchronous, acting as a commitment mechanism. Therefore, it can enhance cooperation and often eliminate inefficient equilibrium outcomes present in the static (normal form) game. Interestingly, (i) this can happen even in a finite game (possibly as short as two periods) and (ii) without reputation building. Furthermore, (iii) the required degree of commitment may be under some circumstances arbitrarily low and under others infinitely high. Our main example comes from macroeconomics in which various rigidities have played a central role. Investigating the Kydland–Prescott–Barro–Gordon monetary policy game, we derive the necessary and sufficient degree of long-term policy commitment to low inflation under which the influential time-inconsistency problem is eliminated.     

THEORY AND PRACTICE IN THE CLASSROOM: A REPEATED GAME OF MULTIMARKET OLIGOPOLY

This article describes a repeated game of multimarket contact, designed to be played throughout an entire term. Besides enjoying reciprocal advantages in their home markets, firms are perfectly informed after every round about each other's decisions. For most of the game, it appears there is always a future in which to punish deviations, and (with the game's parameters) zero-cost punishments can always be implemented. Thus the game provides all the elements for an escape from the prisoner's dilemma. Theoretical foundations, predictions, and some results are also discussed.     

Purely procedural preferences - Beyond procedural equity and reciprocity

We conduct experiments in which parties face a pair of two-player pie-splitting procedures. Parties submit their strategy in each, their beliefs about their opponent's choices, and are also asked whether they prefer one procedure over the other. The procedures – a yes-no game, an ultimatum game, and a dictator game – are designed such that by all existing economic preference models, whether distributive or procedural, parties should be indifferent between them. In particular, the procedures should yield the same outcomes, the same expected outcomes and carry the same information on parties' intentions. At the same time, the procedures differ in the way they distribute decision and information rights across players, and also in their complexity and efficiency. Experimentally, parties do indeed still reveal preferences over the procedures at hand. To explore why this happens, we elicit individuals' simplicity and efficiency ratings of the procedures, and also the degree by which individuals invoke the equality of basic rights and liberties in their moral judgement – an ethical criterion not yet captured by any preference model. The preferences we find link to this data. We explore formalizations for such preferences.     

Endogenous Games and Mechanisms: Side Payments Among Players

We characterize the outcomes of games when players may make binding offers of strategy contingent side payments before the game is played. This does not always lead to efficient outcomes, despite complete information and costless contracting. The characterizations are illustrated in a series of examples, including voluntary contribution public good games, Cournot and Bertrand oligopoly, principal–agent problems, and commons games, among others.