Payoff Asymmetries Research Articles

Communication in stag hunt games: When does it really help?

This paper examines whether the effectiveness of cheap-talk communication in Stag-Hunt-like games is influenced by payoff asymmetry between players. We find that communication improves efficiency when both players benefit from the Pareto-dominant equilibrium. Otherwise, its impact is limited, regardless of whether one or both players communicate their intended actions.

Revisiting the Asymmetric Matching Pennies Contradiction in China.

The asymmetric matching pennies contradiction posits that contrary to the prediction of mixed-strategy Nash equilibrium, experimental subjects' choices are, in practice, based heavily on the magnitudes of their own payoffs. Own-payoff effects are robustly confirmed in the literature. Closely following the experimental setups in the literature which support the contradiction, we conduct a series of asymmetric matching pennies games in China, hypothesizing play which is closer to equilibrium frequencies than previously found. Contrary to previous experiments which were conducted in the United States, we find that there are essentially no own-payoff effects among Row players who face large payoff asymmetry. In a Quantal Response Equilibrium framework allowing for altruism or spite, the behavior of our subjects corresponded to a positive spite parameter, whereas the results of previous studies corresponded to altruism. Our results may be consistent with recent psychology literature that finds people from collectivist cultures are substantially more adept at taking the perspective of others compared with people from individualist cultures, a feature of the reasoning needed to obtain mixed-strategy equilibrium.

Either with us or against us: experimental evidence on partial cartels

This paper analyzes the coordination challenge a partial cartel faces when payoff asymmetries between potential cartel insiders and potential cartel outsiders are large. We introduce two experimental treatments: a standard treatment where a complete cartel can be supported in a Nash equilibrium and a modified treatment where a complete cartel and a partial cartel can both be supported in a Nash equilibrium. To assess the role of communication both treatments are additionally run with a “chat option,” yielding four treatments in total. Our results show that subjects frequently reject the formation of partial cartels in the modified treatments. In all treatments with communication subjects are more likely to form complete cartels than partial cartels. The implications of these results are important for antitrust: payoff asymmetries between cartel members and outsiders may jeopardize the formation of partial cartels. Yet complete cartels may be formed instead, if institutional mechanisms with frequent communication are used to form cartels.

The emergence of conventions in the repeated volunteer's dilemma: The role of social value orientation, payoff asymmetries and focal points

Conventions are arbitrary rules of behavior that coordinate social interactions. Here we study the effects of individuals' social value orientations (SVO) and situational conditions on the emergence of conventions in the three-person volunteer's dilemma (VOD). The VOD is a step-level collective good game in which only one actor's action is required to produce a benefit for the group. It has been shown that if actors interact in the payoff-symmetric VOD repeatedly, a turn-taking convention emerges, resulting in an equal distribution of payoffs. If the VOD is asymmetric, with one “strong” actor having lower costs of volunteering, a solitary-volunteering convention emerges by which the strong actor volunteers earning less than others. In study 1 we test whether SVO promotes turn-taking and hampers solitary-volunteering. We find that groups with more prosocials engage less in turn-taking and no effect of SVO on the emergence of solitary-volunteering. In study 2 we test whether making one actor focal is sufficient for solitary-volunteering to emerge. We find instead that payoff asymmetry with one strong actor is a necessary precondition. We discuss explanations for our findings and propose directions for future research.

GLOBAL GAMES WITH STRATEGIC SUBSTITUTES

AbstractWe study global games with strategic substitutes. Specifically, for a class of binary‐action, ‐player games with strategic substitutes, we prove that under payoff asymmetry, as incomplete information vanishes, the global games approach selects a unique equilibrium. We characterize this equilibrium profile ; players employ switching strategies at different cutoff signals, the order of which is directly determined by payoff asymmetry. We provide examples that illustrate our result and its connection with dominance solvability. We extend the global game literature, which has thus far been developed for games with strategic complementarities, to new applications in industrial organization, collective action problems, finance, etc .

The conflict-cooperation effect persists under intragroup payoff asymmetry

In real-world intergroup conflict, not all in-group members are equally threatened by the out-group. Yet, the impact of intragroup payoff asymmetry on the inclination to mutually cooperate during intergroup conflict and therefore to protect against out-group attacks, i.e., the “conflict-cooperation effect,” has not been investigated so far. In Study 1, we replicate previous research by using a novel experimental game paradigm, showing increased intragroup cooperation in the presence (vs. absence) of out-group threat under intragroup payoff symmetry. In Study 2, we find a conflict-cooperation effect among group members who are threatened (victims) as well as among group members who are not threatened (helpers) by the out-group. Intragroup cohesiveness, i.e., perceived closeness among in-group members, mediates the conflict-cooperation effect, particularly among selfishly-oriented individuals. Our results support the notion that intergroup conflict may have favored the evolutionary adaption of intragroup cooperation even when the in-group members were asymmetrically threatened by intergroup conflict.

Market Power and Welfare in Asymmetric Divisible Good Auctions

We analyze a divisible good uniform-price auction that features two groups each with a finite number of identical bidders. Equilibrium is unique, and the relative market power of a group increases with the precision of its private information but declines with its transaction costs. In line with empirical evidence, we find that an increase in transaction costs and/or a decrease in the precision of a bidding group's information induces a strategic response from the other group, which thereafter attenuates its response to both private information and prices. A stronger bidding group -which has more precise private information, faces lower transaction costs, and is more oligopsonistic- has more market power and so will behave competitively only if it receives a higher per capita subsidy rate. When the strong group values the asset no less than the weak group, the expected deadweight loss increases with the quantity auctioned and also with the degree of payoff asymmetries. Market power and the deadweight loss may be negatively associated.

Pretrial settlement and coercion: An experiment

Pretrial settlements attempts can be either freely chosen by litigating parties or imposed to them, notably by law or by a judge, which renders the settlement stage mandatory in the latter case, as in mandatory mediation procedures. In a lab experiment, we first analyze the determinants of the litigants’ willingness to bargain. Then we investigate the impact of a bargaining obligation on the litigants’ behavior during the negotiation, by varying both the probability that the constraint is enforced and payoff asymmetry between parties. We show that the willingness to bargain depends on one's relative advantage in terms of expected judgment levels (after or instead of a pretrial settlement attempt), on gender and on the probability of being effectively constrained. We also highlight that players who are forced to bargain are more inclined to concessions within the negotiation than the pairs which freely bargain. Finally, we show that forced bargaining leads to more egalitarian agreements. Our results may have important implications in terms of public policy regarding mandatory mediation.

Payoff- and Sex-Biased Social Learning Interact in a Wild Primate Population

Social learning in animals is now well documented, but few studies have determined the contexts shaping when social learning is deployed. Theoretical studies predict copying of conspecifics gaining higher payoffs [1-4], a bias demonstrated in primates only in captivity [5]. In the wild, research has shown selective attention toward the philopatric sex, a group's stable core [6]. Here, we report the first rigorous experimental test of the existence of a payoff bias in wild primates and its interaction with the sex of the model. We created a payoff bias in which an immigrant alpha male in each of three groups of wild vervet monkeys received five times more food upon opening a foraging box than did the philopatric alpha female, whereas in two control groups, male and female models received the same amount of food. We tested whether this payoff asymmetry would override thepreviously documented selective learning from resident females. Group members were tested after having watched both models. When both models received the same amount of food, audience members copied the female model significantly more than the male model, confirming previous findings. However, when a marked payoff bias was introduced, male, but not female, vervet monkeys significantly more often copied the male model receiving a higher payoff. These results demonstrate behavioral flexibility in the dispersing sex in these primates and suggest that the philopatric sex can afford to be more conservative in their social learning. Our findings show that multiple social-learning biases can coexist and interact within the same species.

Payoff inequity reduces the effectiveness of correlated-equilibrium recommendations

We examine theoretically and experimentally how individuals’ willingness to follow third-party recommendations in 2 × 2 games is affected by payoff asymmetry. We consider six versions of Battle-of-the-Sexes. Recommendations imply monetary payoffs that are equal ex ante, but unequal ex post. So, although following recommendations constitutes a Nash equilibrium under standard preferences, sufficiently inequity-averse players can rationally disobey a recommendation that would lead to a very unfavourable payoff distribution, as long as the cost of doing so is not too large. Our theoretical model incorporates inequity aversion, along with level-k reasoning. Our main experimental result is consistent with the model: as either payoff asymmetry increases or the cost of disobeying an unfavourable recommendation decreases, subjects are more likely to disobey recommendations.

Market Power and Welfare in Asymmetric Divisible Good Auctions

We analyze a divisible good uniform-price auction that features two groups each with a finite number of identical bidders. Equilibrium is unique, and the relative market power of a group increases with the precision of its private information but declines with its transaction costs. In line with empirical evidence, we find that an increase in transaction costs and/or a decrease in the precision of a bidding group.s information induces a strategic response from the other group, which thereafter attenuates its response to both private information and prices. A “stronger” bidding group - which has more precise private information, faces lower transaction costs, and is more oligopsonistic - has more market power and so will behave competitively only if it receives a higher per capita subsidy rate. When the strong group values the asset no less than the weak group, the expected dead-weight loss increases with the quantity auctioned and also with the degree of payoff asymmetries. Market power and the dead-weight loss may be negatively associated.

Exploring the Motivations for Punishment: Framing and Country-Level Effects.

Identifying the motives underpinning punishment is crucial for understanding its evolved function. In principle, punishment of distributional inequality could be motivated by the desire to reciprocate losses ('revenge') or by the desire to reduce payoff asymmetries between the punisher and the target ('inequality aversion'). By separating these two possible motivations, recent work suggests that punishment is more likely to be motivated by disadvantageous inequality aversion than by a desire for revenge. Nevertheless, these findings have not consistently replicated across different studies. Here, we suggest that considering country of origin—previously overlooked as a possible source of variation in responses—is important for understanding when and why individuals punish one another. We conducted a two-player stealing game with punishment, using data from 2,400 subjects recruited from the USA and India. US-based subjects punished in response to losses and disadvantageous inequality, but seldom invested in antisocial punishment (defined here as punishment of non-stealing partners). India-based subjects, on the other hand, punished at higher levels than US-based subjects and, so long as they did not experience disadvantageous inequality, punished stealing and non-stealing partners indiscriminately. Nevertheless, as in the USA, when stealing resulted in disadvantageous inequality, India-based subjects punished stealing partners more than non-stealing partners. These results are consistent with the hypothesis that variation in punitive behavior varies across societies, and support the idea that punishment might sometimes function to improve relative status, rather than to enforce cooperation.

Resource availability and predation risk influence contest behavior and dominance hierarchies in crayfish

Theory-based predictions on asymmetries in animal contests have seldom been tested in situations where payoff asymmetries exist among contestants otherwise clearly matched for physical fighting capacity (i.e., resource holding potential, RHP). We examined the effects of food availability and predation risk on contest outcomes and the maintenance of dominance hierarchies in size-matched male noble crayfish pairs (Astacus astacus). Following theoretical predictions, dominant status established via contests staged in a non-resource context successfully predicted contest outcome (resource use) once resources were made available. Still, resource availability significantly increased the aggressive motivation of subordinates and sometimes resulted in hierarchy reversals. In subsequent resource-based contests, subordinates increased their fighting intensity, whereas dominants reduced their fighting motivation, potentially reflecting hunger-driven payoff asymmetries. Moreover, the data support the “asset-protection” principle by showing for the first time that predation risk lowered the aggressive motivation of dominants. At the same time, the percentage of fighting bouts won by subordinates increased significantly, leading to reversal of prior dominance relationships in 30 % of pairs. Compared to pairs where the hierarchy was retained through the different contests, pairs where dominance was reversed were characterized by smaller RHP asymmetries, which is again consistent with theory. These results show how animal contest behavior can be sensitive to the complex interactive effects of prior experience, resource value and RHP. Furthermore, in systems where repeated contests lead to dominance hierarchies, reversals within the hierarchy may occur more often when the RHP asymmetry between contestants is small. Contest outcome and resulting dominance status of contestants may be influenced by relative resource value and perceived costs involved in animal contests, especially when individuals are similar in major correlates of fighting ability, i.e., often body and weapon size. However, empirical evidence is scant. Using size-matched male crayfish pairs, we investigated the effects of food availability and predation threat on fighting behavior on individual and pair level and on hierarchy maintenance in repeated contests. Our study reveals novel evidence, indicating that crayfish are capable of changing their decisions during contests in response to food availability and predation threat, which can alter the hierarchy. For example, dominants reduced their aggressiveness in the presence of predation threat. Overall, hierarchy reversals were more likely in pairs where the difference in fighting ability between contestants was smaller.

Assessment of post-merger coordinated effects: Characterization by simulations

This paper aims at evaluating the coordinated effects of horizontal mergers by simulating their impact on firms’ critical discount factors. We consider a random coefficient model on the demand side and heterogeneous price-setting firms on the supply side. Results suggest that mergers strengthen the incentives to collude of the merged firm, but weaken the incentives of non-merging parties, with the former effect being stronger. To assess the magnitudes of these effects, we introduce the concepts of Asymmetry in Payoffs and Change in Payoffs effects, which allow us to identify appropriate screening tools according to the relative pre-merger payoffs of merging parties.

Effects of group size and contest location on the outcome and intensity of intergroup contests in wild blue monkeys

Intergroup contests determine access to resources and influence the evolution of group living in social species. Asymmetries in resource-holding potential and payoffs should influence the outcome and intensity of such contests. We evaluated predictors of contest outcome and intensity using data collected over 40 months from 6 groups of wild blue monkeys, Cercopithecus mitis. We found increased odds of winning when a group was larger and used the contest site more than its opponent, and when contests occurred closer to the group's home range centre while farther from the opponent's centre. However, a larger difference in group size (across five pairs of opposing groups) did not predict a greater proportion of contests won by the larger group. Some evidence suggested increased odds of a draw when group sizes were more similar. In addition, contests were longer and more aggressive when groups were more similar in size and when the contest site was similarly central in both groups' home ranges. Contests were also more aggressive when the opposing groups' use of the contest site was more similar. Overall, asymmetries in resource-holding potential (i.e. group size) and/or payoffs related to the contest's location influenced a group's competitive advantage, the likelihood of a draw and the intensity of intergroup contests. Although comparable data are limited, it seems clear that both types of asymmetries can play a role in determining the outcome and intensity of intergroup contests, and that the relative power of each may vary across species.

Individual participation in intergroup contests is mediated by numerical assessment strategies in black howler and tufted capuchin monkeys.

Asymmetries in resource-holding potential between opposing groups frequently determine outcomes of intergroup contests. Since both numerical superiority and high intergroup dominance rank may confer competitive advantages, group members should benefit from assessing the relative strength of rivals prior to engaging in defensive displays. However, differences in individual assessment may emerge when cost-benefit trade-offs differ among group members. We examine the influence of numerical superiority and intergroup dominance relationships on individual participation in intergroup encounters in black howler monkeys (Alouatta pigra) and tufted capuchin monkeys (Sapajus nigritus). Black howlers responded with longer vocal displays during encounters with neighbours with an equal number of resident males, while tufted capuchins increased their participation with increasing relative male group size. Within each species, males and females responded similarly to varying numerical odds, suggesting that despite pay-off asymmetries between males and females, both sexes were similarly influenced by numerical asymmetries in deciding to participate in collective group defence. Whereas the outcome of contests among tufted capuchins was determined by relative male group size, reflected in a pronounced intergroup dominance hierarchy, the absence of dominance relationships among black howler groups may have provoked prolonged vocal displays in order to assess rival groups with matching competitive abilities.

The good of the few: Reciprocal acts and the provision of a public bad

People trade favors when doing so increases efficiency. Will they when it reduces efficiency, such as in political logrolling? We introduce the “Stakeholder Public Bad” game, in which common fund contributions increase one person's earnings (the “Stakeholder”) while reducing others’ earnings and overall efficiency. The Stakeholder position rotates through all group members or just alternates among two people (making it easier to form a coalition). High Stakeholder rewards provide a lever for reciprocity: if someone contributes when another is Stakeholder, he may be rewarded with a gift when he becomes Stakeholder. Reciprocity is only possible when agents know others’ roles and actions, so information provision may be pro- or anti-social. In a laboratory experiment, we combine a rotating or alternating asymmetry in payoffs with varying levels of information provision to examine pro- and anti-social reciprocity. We find that subjects in the Stakeholder role willingly sacrifice social welfare. We also see both anti-social and pro-social favor trading, particularly when coalition-forming is easier. Favor trading does not change the mean level of public bad provision. People who trade favors tend to be less risk averse.

Exit Option Can Make Cooperation Easier

In the modern society, mobility of players has increased dramatically. It is important to extend game theory to endogenize the set of players. In this paper, we extend the repeated n-person Prisoner's Dilemma by allowing some or all players to exit after each period and analyze how mobility affects endogenous cooperation in a fundamental sense: players voluntarily participate in the game and act non-myopically. We characterize the parameters (the allocation of exit options among players and the payoffs) under which eternal universal cooperation is sustained at a discount factor lower than the one for the ordinary repeated Prisoner's Dilemma. Factors that enhance endogenous long-term cooperation include payoff asymmetry in the Prisoner's Dilemma, multiple mobile players who have the exit option, and immobile players having low after-game payoffs. These are new insights which give policy implications on employment relationships and other voluntary partnership situations as well.

Fairness Norms Can Explain the Emergence of Specific Cooperation Norms in the Battle of the Prisoner's Dilemma

Cooperation norms often emerge in situations, where the long term collective benefits help to overcome short run individual interests, for instance in repeated Prisoner's Dilemma (PD) situations. Often, however, there are different paths to cooperation, benefiting different kinds of actors to different degrees. This leads to payoff asymmetries even in the state of cooperation, and consequently can give rise to normative conflicts about which norms should be in place. This norm coordination problem will be modeled as a Battle of the Sexes game (BoS) with different degrees of asymmetry in payoffs. I combine the PD and the BoS to the 3 × 3 Battle of the Prisoner's Dilemma (BOPD) with several asymmetric cooperative and 1 noncooperative equilibria. Game theoretical and “behavioral” predictions are derived about the kind of norms that are likely to emerge under different shadows of the future and degrees of asymmetry and tested in a lab experiment. The experimental data show that game theory fairly well predicts the basic main effects of the experimental manipulations but “behavioral” predictions perform better in describing the equilibrium selection process of emerging norms.

Corporate Social Responsibility or Payoff Asymmetry? A Study of an Endogenous Timing Game

We revisit an endogenous timing game by introducing corporate social responsibility into firms' payoffs. Previous research investigates an endogenous timing game in a mixed oligopoly, wherein one welfare‐maximizing public firm competes against profit‐maximizing private firms. It shows that the outcome is completely different from that of private oligopoly. In contrast to its result, we find that this change in payoff does not matter as long as the payoffs are symmetric. Our result indicates that asymmetry, and not welfare‐concerning objectives, yields specific results in the literature on mixed oligopoly.