The effect of payoff tables on experimental oligopoly behavior

We explore the effects of the provision of an information-processing instrument—payoff tables—on behavior in experimental oligopolies. In one experimental setting, subjects have access to payoff tables whereas in the other setting they have not. It turns out that this minor variation in presentation has non-negligible effects on participants’ behavior, particularly in the initial phase of the experiment. In the presence of payoff tables, subjects tend to be more cooperative. As a consequence, collusive behavior is more likely and quickly to occur.     

What does “clean” really mean? The implicit framing of decontextualized experiments

It is standard in experimental economics to use decontextualized designs where payoff structures are presented using neutral language. Here we show that cooperation in such a neutrally framed Prisoner’s Dilemma is equivalent to a PD framed as contributing to a cooperative endeavour. Conversely, there is substantially less cooperation in a PD framed as a competition. We conclude that in a decontextualized context, our participants by default project a cooperative frame onto the payoff structure.     

Conditional behavior and learning in similar stag hunt games

This paper reports an experiment using Stag Hunt games with different payoff ranges. Specifically, in one treatment for half of the games the payoff dominant and the risk dominant equilibrium coincide and for the other half of the games they conflict; in the second treatment they always conflict. The experiment provides evidence that the payoff range experienced by the participant influences the likelihood of efficient conventions emerging. In particular, experiencing games where payoff dominance and risk dominance coincide appears to make payoff dominance more attractive in games in which they conflict. In the experiment, we also observe conditional behavior emerging with experience. We develop a model of conditional expectations to explain these stylized facts that depends crucially on the assumption that after a brief learning period participants categorize their experience using the same relative bandwidth in both treatments even though the range of experience is twice as large in treatment 1 as it is in treatment 2. The assumption cannot be rejected by the data. The analysis provides a formal example in which increasing experienced diversity by changing the way similar experiences are categorized increases the likelihood of efficient conventions emerging in communities playing similar Stag Hunt games.     

Patience auctions: the impact of time vs. money bidding on elicited discount rates

We introduce, test, and compare two auction-based methods for eliciting discount rates. In these “patience auctions”, participants bid the smallest future sum they would prefer -or- the longest time they would wait for a reward, rather than receive a smaller, immediate payoff. The most patient bidder receives the delayed reward; all others receive the immediate payoff. These auctions allow us to compare discounting when participants’ attention is focused on the temporal versus monetary dimension of delayed rewards. We find that the estimated parameters in the three most commonly used discount functions (exponential, hyperbolic, and quasi-hyperbolic) differ across these two bidding methods (time-bids vs. money-bids). Specifically, our participants tend to show more impatience under time-bids. Furthermore, we find that people are more likely to exhibit exponential (as opposed to hyperbolic) discounting and exhibit less present bias under time-bids, compared to money-bids. To our knowledge, this paper is the first to directly compare time versus money preference elicitations, within the same subjects, using an incentive-compatible mechanism.     

Technology adoption in markets with network effects: Theory and experimental evidence

We examine a technology-adoption game with network effects in which coordination on either technology A or technology B constitutes a Nash equilibrium. Coordination on technology B is assumed to be payoff dominant. We define a technology’s critical mass as the minimal share of users, which is necessary to make the choice of this technology the best response for any remaining user. We show that the technology with the lower critical mass implies risk dominance and selection by the maximin criterion. We present experimental evidence that both payoff dominance and risk dominance explain participants’ choices in the technology-adoption game. The relative riskiness of a technology can be proxied using either technologies’ critical masses or stand-alone values absent any network effects.     

The law of supply in games, markets and matching models

Summary In large games with transferable utility, core payoffs satisfy a comparative statics property: If the proportion of one type of player increases, then the core payoff to that type of player decreases (does not increase). Markets with transferable utility satisfy a similar property: if the aggregate supply of a commodity increases, its value relative to the value of all commodities decreases. In market games, if one type of agent becomes more plentiful, his competitive payoff falls, and its decrease is engineered by a decrease in the relative value of his endowment.We thank Bob Anderson, Joe Farrell, Steve Goldman, Chris Shannon, seminar participants of the Mathematical Economics Seminar at Berkeley (August 1994), the University of Pittsburg (November 1994), Tel Aviv University and the Institute on Rationality at the Hebrew University (January 1995), and especially Vince Crawford for useful discussion.     

Risk Attitudes of Children and Adults: Choices Over Small and Large Probability Gains and Losses

In this paper we examine how risk attitudes change with age. We present participants from age 5 to 64 with choices between simple gambles and the expected value of the gambles. The gambles are over both gains and losses, and vary in the probability of the non-zero payoff. Surprisingly, we find that many participants are risk seeking when faced with high-probability prospects over gains and risk averse when faced with small-probability prospects. Over losses we find the exact opposite. Children's choices are consistent with the underweighting of low-probability events and the overweighting of high-probability ones. This tendency diminishes with age, and on average adults appear to use the objective probability when evaluating risky prospects.     

Equivalence of strong and coalition-proof Nash equilibria in games without spillovers

Summary This paper examines the conditions which guarantee that the set of coalition-proof Nash equilibria coincides with the set of strong Nash equilibria in the normal form games withoutspillovers. We find thatpopulation monotonicity properties of the payoff functions, when the payoff of a player changes monotonically when the size of the group of players choosing the same strategy increases, are crucial to obtain the equivalence of these two solution concepts. We identify the classes of games, satisfying population monotonicity properties, which yield the equivalence of the set of coalition-proof Nash equilibria and the set of strong Nash equilibria. We also provide sufficient conditions for the equivalence result even when the population monotonicity assumptions are relaxed.We wish to thank Mamoru Kaneko, Akihiko Matsui, Tomoichi Shinotsuka, Benyamin Shitoviz, Tayfun Sonmez, William Thomson, the participants of the Southeastern Economic Theory Meeting in Charlottesville and the seminars at CORE and University of Tsukuba for useful discussions and comments. Our special thanks due anonymous referee for the suggestion to add a section addressing the issue of existence of a strong Nash equilibrium.     

Reputation with equal discounting in repeated games with strictly conflicting interests

We analyze reputation effects in two-player repeated games of strictly conflicting interests. In such games, player 1 has a commitment action such that a best reply to it gives player 1 the highest individually rational payoff and player 2 the minmax payoff. Players have equal discount factors. With positive probability player 1 is a type who chooses the commitment action after every history. We show that player 1's payoff converges to the maximally feasible payoff when the discount factor converges to one. This contrasts with failures of reputation effects for equal discount factors that have been demonstrated in the literature.     

Excess payoff dynamics and other well-behaved evolutionary dynamics

We consider a model of evolution in games in which agents occasionally receive opportunities to switch strategies, choosing between them using a probabilistic rule. Both the rate at which revision opportunities arrive and the probabilities with which each strategy is chosen are functions of current normalized payoffs. We call the aggregate dynamics induced by this model excess payoff dynamics. We show that every excess payoff dynamic is well-behaved: regardless of the underlying game, each excess payoff dynamic admits unique solution trajectories that vary continuously with the initial state, identifies rest points with Nash equilibria, and respects a basic payoff monotonicity property. We show how excess payoff dynamics can be used to construct well-behaved modifications of imitative dynamics, and relate them to two other well-behaved dynamics based on projections.     

Endogenous order and information aggregation

Privately informed experts with heterogeneous expertise decide when to give advice and what advice to give. Each expert’s utility depends upon that expert’s own message as well as those of the other experts. Under different forms of payoff externalities, we find varying results for the optimal order in which messages are sent and the existence of herd behavior. Under negative payoff externalities, all experts send a message together without any delay and a herd never arises. This leads to truthful revealing of all private information. Without forcing any order of speech, we obtain a result similar to the ‘anti-seniority rule’. This, however, goes in the opposite direction when positive payoff externalities are induced. An incentive structure with positive payoff externalities gives rise to a herd led by the most precise expert with a delay in the disclosure of information. Next, we test for the nature of payoff externalities in the remuneration of forecasters listed with I/B/E/S. We find that the underlying payoff externalities are negative, i.e. the benefit from making dissimilar forecasts is higher than that from making similar ones.     

An examination of the effect of messages on cooperation under double-blind and single-blind payoff procedures

Previous research has suggested that communication and especially promises increase cooperation in laboratory experiments. This has been taken as evidence for internal motivations such as guilt aversion or preference for promise keeping. The goal of this paper was to examine messages under a double-blind payoff procedure to test the alternative explanation that promise keeping is due to external influence and reputational concerns. Employing a 2×2 design, we find no evidence that communication increases the overall level of cooperation in our experiments with double-blind payoff procedures. However, we also find no evidence that communication impacts cooperation in our experiments with single-blind payoff procedures. Further, the payoff procedure does not appear to impact aggregate cooperation.     

Information, trade and incomplete markets

The no-trade result of Milgrom and Stokey, J Econ Theory 26:17–27 (1982), states that if rational traders begin with an ex-ante Pareto optimal allocation then the arrival of information cannot generate trade. This paper allows traders to trade before and after the arrival of information. If there are enough securities to hedge against all payoff relevant risk, then the preinformation-arrival allocation is Pareto optimal and information arrival has no effect. This no-retrade result is the competitive analog of the no-trade result of (1982). However, information generically generates trade when markets are state-contingent incomplete.We thank seminar participants at Cambridge, Carnegie Mellon,Cornell, Essex, London, Maastricht, USC, and York and participants at the 2003 SITE, the 2003 SAET and the Fall 2002 Cornell–Penn State Macro Conference. We also thank Karl Shell and a referee for this journal for useful comments     

Rotating Savings and Credit Associations When Participants are Risk Averse*

We model rotating savings and credit associations (Roscas) among risk‐averse participants who experience privately observed income shocks. A random Rosca is not advantageous, whereas a bidding Rosca is if temporal risk aversion is less pronounced than static risk aversion. The payoff scheme of a bidding Rosca facilitates risk sharing in the presence of information asymmetries. The risk‐sharing performance of a simple arrangement where a group of homogenous individuals runs several bidding Roscas simultaneously is as good as that of a linear risk‐sharing contract, and is more enforceable because it carries a fixed rather than a variable contribution.     

Sowing Doubt Optimally in Two-Person Repeated Games

Consider a two-person repeated game, where one of the players, P1, can sow doubt, in the mind of his opponent, as to what P1's payoffs are. This results in a two-person repeated game with incomplete information. By sowing doubt, P1 can sometimes increase his minimal equilibrium payoff in the original game. We prove that this minimum is maximal when only one payoff matrix, the negative of the payoff matrix of the opponent, is added (the opponent thus believes that he might play a zero-sum game). We obtain two formulas for calculating this maximal minimum payoff. Journal of Economic Literature Classification Numbers: C7, D8.     

Robust rational turnout

We show that equilibria of a class of participation games (Palfrey and Rosenthal in Public Choice 41(1):7–53, 1983; Journal of Public Economics 24(2):171–193, 1984) exhibit minimal heterogeneity of behavior so that players’ mixed strategies are summarized by at most two probabilities. We then establish that, except for a finite set of common costs of participation, these games are regular. Thus, equilibria of these voting games are robust to general payoff perturbations and survive in nearby games of incomplete information. Thanks to participants of the 2006 MPSA conference for comments on an early version.     

Endogenous timing in the presence of non-monotonicities

The aim of this paper is to generalize the endogenous timing game proposed by Hamilton and Slutsky (Games and Economic Behavior, 1990, 2, pp. 29–46) by allowing the payoff or the marginal payoff of a player to become non-monotonic with respect to the strategy of the opponent. We propose a taxonomy of the subgame-perfect Nash equilibria based on the characteristics of the payoff functions proposed by Eaton (Canadian Journal of Economics, 2004, 37, pp. 805–29). We determine under which conditions of the initial payoff functions commitment has a social value and when the simultaneous-move Nash equilibrium is commitment robust and discuss its Pareto efficiency.     

Communication in repeated network games with imperfect monitoring

I consider repeated games with private monitoring played on a network. Each player has a set of neighbors with whom he interacts: a player's payoff depends on his own and his neighbors' actions only. Monitoring is private and imperfect: each player observes his stage payoff but not the actions of his neighbors. Players can communicate costlessly at each stage: communication can be public, private or a mixture of both. Payoffs are assumed to be sensitive to unilateral deviations. First, for any network, a folk theorem holds if some Joint Pairwise Identifiability condition regarding payoff functions is satisfied. Second, a necessary and sufficient condition on the network topology for a folk theorem to hold for all payoff functions is that no two players have the same set of neighbors not counting each other.     

Freedom, enforcement, and the social dilemma of strong altruism

Cooperation in joint enterprises poses a social dilemma. How can altruistic behavior be sustained if selfish alternatives provide a higher payoff? This social dilemma can be overcome by the threat of sanctions. But a sanctioning system is itself a public good and poses a second-order social dilemma. In this paper, we show by means of deterministic and stochastic evolutionary game theory that imitation-driven evolution can lead to the emergence of cooperation based on punishment, provided the participation in the joint enterprise is not compulsory. This surprising result—cooperation can be enforced if participation is voluntary—holds even in the case of ‘strong altruism’, when the benefits of a player’s contribution are reaped by the other participants only.     

An investment game with third-party intervention

This paper explores the effect of the possibility of third-party intervention on behavior in a variant of the Berg et al. [Berg, J., Dickhaut, J., McCabe, K., 1995. Trust, reciprocity and social history. Games and Economic Behavior 10, 122–142] “Investment Game”. A third-party's material payoff is not affected by the decisions made by the other participants, but this person may choose to punish a responder who has been overly selfish. The concern over this possibility may serve to discipline potentially selfish responders. We also explore a treatment in which the third party may also choose to reward a sender who has received a low net payoff as a result of the responder's action. We find a strong and significant effect of third-party punishment in both punishment regimes, as the amount sent by the first mover is more than 60% higher when there is the possibility of third-party punishment. We also find that responders return a higher proportion of the amount sent to them when there is the possibility of punishment, with this proportion slightly higher when reward is not feasible. Finally, third parties punish less when reward is feasible, but nevertheless spend more on the combination of reward and punishment when these are both permitted than on punishment when this is the only choice for redressing material outcomes.