Games, Volume 12, Issue 2 (June 2021) – 22 articles

The exit of the United Kingdom from the European Union has had profound economic and political effects. Here, we look at a particular aspect, the power distribution in the Council of the European Union. Using the Shapley–Shubik power index, we calculate the member states’ powers with and without the United Kingdom and update earlier power forecasts using the Eurostat’s latest population projections. There is a remarkably sharp relation between population size and the change in power: Brexit increases the largest members’ powers while decreasing the smallest ones’ powers. Full article

Peer punishment is widely lauded as a decentralized solution to the problem of social cooperation. However, experimental evidence of its effectiveness primarily stems from public good structures. This paper explores peer punishment in another structural setting: a system of generalized exchange. In a laboratory experiment, a repeated four-player prisoner’s dilemma is arranged either in a public good structure or in a circular network of generalized exchange. The experimental results demonstrate that the merits of peer punishment do not extend to generalized exchange. In the public good, peer punishment was primarily altruistic, was sensitive to costs, and promoted cooperation. In generalized exchange, peer punishment was also altruistic and relatively frequent, but did not increase cooperation. While the dense punishment network underlying the public good facilitates norm enforcement, generalized exchange decreases control over norm violators and reduces the capacity of peer punishment. I conclude that generalized exchange systems require stronger forms of punishment to sustain social cooperation. Full article

The emergence of the modern gig economy introduces a new set of employment considerations for firms and laborers that include various trade-offs. With a game-theoretical approach, we examine the influences of technology, policy and markets on firm and worker preferences for gig labor. Theoretically, we present new conceptual extensions to the replicator equation and model oscillating dynamics in two-player asymmetric bi-matrix games with time-evolving environments, introducing concepts of the attractor arc, trapping zone and escape. While canonical applications of evolutionary game theory focus on the evolutionary stable strategy, our model assumes that the system exhibits oscillatory dynamics and can persist for long temporal intervals in a pseudo-stable state. We demonstrate how changing market conditions result in distinct evolutionary patterns across labor economies. Informing tensions regarding the future of this new employment category, we present a novel payoff framework to analyze the role of technology on the growth of the gig economy. Regarding governance, we explore regulatory implications within the gig economy, demonstrating how intervals of lenient and strict policy alter firm and worker sensitivities between gig and employee labor strategies. Finally, we establish an aggregate economic framework to explain how technology, policy and market environments engage in an interlocking dance, a balancing act, to sustain the observable co-existence of gig and employee labor strategies. Full article

This paper tests the hypothesis that a (partial) reason why cartels—collective but costly and non-binding price agreements—lead to higher prices in a Bertrand oligopoly could be because of a selection effect: decision-makers who are willing to form price agreements are more likely to be less competitive and pick higher prices in general. To test this hypothesis we run an experiment where participants play two consecutive Bertrand pricing games: first a standard version without the opportunity to form agreements; followed by a version where participants can vote whether to have a (costly) non-binding agreement as a group to pick the highest number. We find no statistically significant difference between the numbers picked in the first game by participants who vote for and against an agreement in the second game. We do confirm that having a non-binding agreement to cooperate leads to higher numbers being picked on average. Both participants who voted for and against the agreement increase the number they pick in situations with an agreement. However, this effect is bigger for participants who voted in favour. Full article

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games—in which the pure strategy space is (potentially uncountably) infinite—is far more challenging. Nonetheless, many real-world domains have continuous action spaces, e.g., where actions refer to an amount of time, money, or other resource that is naturally modeled as being real-valued as opposed to integral. We present a new algorithm for approximating Nash equilibrium strategies in continuous games. In addition to two-player zero-sum games, our algorithm also applies to multiplayer games and games with imperfect information. We experiment with our algorithm on a continuous imperfect-information Blotto game, in which two players distribute resources over multiple battlefields. Blotto games have frequently been used to model national security scenarios and have also been applied to electoral competition and auction theory. Experiments show that our algorithm is able to quickly compute close approximations of Nash equilibrium strategies for this game. Full article

We present an agent-based model of manipulating prices in financial markets through spoofing: submitting spurious orders to mislead traders who learn from the order book. Our model captures a complex market environment for a single security, whose common value is given by a dynamic fundamental time series. Agents trade through a limit-order book, based on their private values and noisy observations of the fundamental. We consider background agents following two types of trading strategies: the non-spoofable zero intelligence (ZI) that ignores the order book and the manipulable heuristic belief learning (HBL) that exploits the order book to predict price outcomes. We conduct empirical game-theoretic analysis upon simulated agent payoffs across parametrically different environments and measure the effect of spoofing on market performance in approximate strategic equilibria. We demonstrate that HBL traders can benefit price discovery and social welfare, but their existence in equilibrium renders a market vulnerable to manipulation: simple spoofing strategies can effectively mislead traders, distort prices and reduce total surplus. Based on this model, we propose to mitigate spoofing from two aspects: (1) mechanism design to disincentivize manipulation; and (2) trading strategy variations to improve the robustness of learning from market information. We evaluate the proposed approaches, taking into account potential strategic responses of agents, and characterize the conditions under which these approaches may deter manipulation and benefit market welfare. Our model provides a way to quantify the effect of spoofing on trading behavior and market efficiency, and thus it can help to evaluate the effectiveness of various market designs and trading strategies in mitigating an important form of market manipulation. Full article

This work aims to provide different perspectives on the relationships between cooperative game theory and the research field concerning climate change dynamics. New results are obtained in the framework of competitive bargaining solutions and related issues, moving from a cooperative approach to a competitive one. Furthermore, the dynamics of balanced and super-balanced games are exposed, with particular reference to coalitions. Some open problems are presented to aid future research in this area. Full article

We investigate gender differences in lying behavior when the opportunity to tell lies is repeated. In specific, we distinguish the situations in which such an opportunity can be planned versus when it comes as a surprise. We utilize data from an existing published research and show that when the opportunity to tell a lie comes as a surprise, then on the first occasion, males lie more than females. However, when telling lies can be planned, then there is no gender difference in telling a lie. When planning is possible, females tell more lies in the first occasion compared to when it is not possible to plan; males do not show such behavior. On the second and final occasion, males tell more lies than females when they either could not plan but had the opportunity to a lie before, or could plan but did not have to tell a lie before. These observations can be interpreted in terms of the gender differences in consistent versus compensatory moral behavior. Full article

We introduce a new class of matching mechanisms—quantile stable mechanisms—that generate stable matchings that can be seen as a compromise between sides of a two-sided market. We show that responsiveness is a sufficient condition for the existence of such mechanisms and that all such mechanisms are distinct. We also analyze the manipulability of these mechanisms by market participants. Full article

We explore how an incremental change in complexity of strategies (“an inch of memory”) in repeated interactions influences the sets of Nash equilibrium (NE) strategy and payoff profiles. For this, we introduce the two most basic setups of repeated games, where players are allowed to use only reactive strategies for which a probability of players’ actions depends only on the opponent’s preceding move. The first game is trivial and inherits equilibria of the stage game since players have only unconditional (memory-less) Reactive Strategies (RSs); in the second one, players also have conditional stochastic RSs. This extension of the strategy sets can be understood as a result of evolution or learning that increases the complexity of strategies. For the game with conditional RSs, we characterize all possible NE profiles in stochastic RSs and find all possible symmetric games admitting these equilibria. By setting the unconditional benchmark as the least symmetric equilibrium payoff profile in memory-less RSs, we demonstrate that for most classes of symmetric stage games, infinitely many equilibria in conditional stochastic RSs (“a mile of equilibria”) Pareto dominate the benchmark. Since there is no folk theorem for RSs, Pareto improvement over the benchmark is the best one can gain with an inch of memory. Full article

The main goal of collective punishment (CP) is the deterrence of future “wrong-doing” by freedom fighters or terrorists, protesters against an authoritative government, polluters, students playing pranks on their teacher, football teams lacking enthusiasm, or soldiers showing cowardice to the enemy. CP could consist of the lockout of workers, additional training units for football teams, increased control of athletes and firms, up to the shooting of fellow villagers of assassins. I investigate two classes of problems. In one class, resistance against an authority is individually costly, but enough resistance can be successful (the production of a public good, for example, higher wages after a strike). In the other case, “resistance” is individually profitable (a criminal activity as pollution) and enough “resistance” produces a public bad. We find that, in the first situation, the announcement of CP never decreases the level of resistance. In the second situation, CP can be successful. Full article

This paper presents the results of an experimental study of takeover auctions with toeholds. Consistent with the theory, we find a positive effect of toeholds on bidding. Such an effect, however, is of a lower magnitude and the bidding premium function has an opposite slope than the theory predicts, which can be attributed both to risk aversion and subjects’ tendency to think of their bids in relative terms. Consistent with the theory we find no cross-bidder toehold effect, however, such a result is inconsistent with the observed bidding function if people expect their opponents to behave the same way as they do. Full article

Knowing the gender of a counterpart can be focal in the willingness to collaborate in team settings that resemble the classic coordination problem. This paper explores whether knowing a co-worker’s gender affects coordination on the mutually beneficial outcome in a socially risky environment. In an experimental setting, subjects play a one-shot stag hunt game framed as a collaborative task in which they can “work together” or “work alone.” We exogenously vary whether workers know the gender of their counterparts pre-play. When gender is revealed, female players tend to gravitate to collaboration and efficient coordination regardless of the knowledge. Males, when knowingly paired with another male, tend to collaborate less, and thus, are less likely to coordinate on the Pareto optimal outcome. These results demonstrate one way that gender focality can lead to inefficient outcomes and provide insight for organizations looking to induce collaboration among workers. Full article

Hypocrisy is the act of claiming moral standards to which one’s own behavior does not conform. Instances of hypocrisy, such as the supposedly green furnishing group IKEA’s selling of furniture made from illegally felled wood, are frequently reported in the media. In a controlled and incentivized experiment, we investigate how observers rate different types of hypocritical behavior and if this judgment also translates into punishment. Results show that observers do, indeed, condemn hypocritical behavior strongly. The aversion to deceptive behavior is, in fact, so strong that even purely self-deceptive behavior is regarded as blameworthy. Observers who score high in the moral identity test have particularly strong reactions to acts of hypocrisy. The moral condemnation of hypocritical behavior, however, fails to produce a proportional amount of punishment. Punishment seems to be driven more by the violation of the norm of fair distribution than by moral pretense. From the viewpoint of positive retributivism, it is problematic if neither formal nor informal punishment follows moral condemnation. Full article

During the pandemic, school districts have adopted hybrid schedules to continue the education of the students while maintaining social distance. In a hybrid schedule, students in the same classroom are usually divided into two groups and students only in the same group can physically attend class together two days a week. School districts do not take preferences of the students/parents over the days they would like to come to school into account during this procedure. In this paper, we propose a solution that divides students into groups based on their preferences. Our solution respects the number of classrooms initially reserved for each grade and enables possible efficiency gains by swapping classrooms across grades. Moreover, when there are two alternative schedules provided for students, our solution is immune to preference manipulations. Full article

Online advertising often involves targeting ads to certain types of consumers where ads are commonly sold by generalized second price auctions. However, such an auction or mechanism could be considered unfair if similar consumers are consistently shown different ads or consistently receive different payoffs. Results show that such ascending bid auctions may result in unfair treatment and additionally that uncertainty regarding an ad’s value can result in inefficiency. An alternative way to assign ads to consumers is presented called the random assignment mechanism. Results show that the random assignment can improve fairness while improving efficiency in some circumstances. Full article

This paper derives a dynamic path of ongoing terror attacks as a function of terrorists’ capacity and a target government’s counterterror capacity. The analysis provides several novel insights and characterizations. First, the effect of counterterror policy is limited. Second, proactive counterterror policy affects the depreciation (fatigue) of terrorists’ capacity, and defensive counterterror policy limits the worst-case scenario. Third, fluctuations in the time path of attacks are a function of terrorists’ time preferences and adjustment costs of changing tactics, which are policy invariant. Indeed, in our model, the oscillations of terror attacks occur irrespective of the government’s counterterror stance. Fourth, collective action inefficiencies associated with the underprovision of proactive counterterror policies and overprovision of defensive ones are further exacerbated by our finding that proactive counterterror policy is the more effective of the two. Hence, the more effective policy is underprovided. Full article

A game between a representative household and a government was analyzed. The household chose which fractions of two currencies to hold, e.g., a national currency such as a Central Bank Digital Currency (CBDC) and a global currency such as Bitcoin or Facebook’s Diem, and chose the tax evasion probability for each currency. The government chose, for each currency, the probability of detecting and prosecuting tax evasion, the tax rate, and the penalty factor imposed on the household when tax evasion was successfully detected and prosecuted. The household′s fraction of the national currency, the government’s monitoring probability of the national currency, and the penalty factor imposed on the global currency, increased in the household′s Cobb Douglas output elasticity for the national currency. The household′s probabilities of tax evasion on both currencies increased in the government’s Cobb Douglas output elasticity for the national currency. The government’s taxation on both currencies decreased in the output elasticity for the national currency. High output elasticity for the national currency eventually induced the government to tax that currency more than the global currency. The household′s probability of tax evasion on the global currency increased in the government’s output elasticity for that currency. The household was less (more) likely to tax evade on the national (global) currency if the government valued taxation and penalty on the national (global) currency. The results are illustrated numerically where each of the eight parameter values was varied relative to a benchmark. Full article

We develop the theory of stability for aggregate matchings used in empirical studies and establish fundamental properties of stable matchings including the result that the set of stable matchings is a non-empty, complete, and distributive lattice. Aggregate matchings are relevant as matching data in revealed preference theory. We present a result on rationalizing a matching data as the median stable matching. Full article

We investigate whether revealing the identities in a public good game that includes a donation incentive leads to higher contributions to the public good. Previous evidence suggests that contributions to a public good increase significantly when these take place in public. Also, the amount of money given in charitable donations seems to be sensitive to the revealing of identities. Using a laboratory experiment, we implement a 20% donation share that is dependent on participants’ contributions to a public good. The donation is either costless (because it is financed by the experimenter) or deducted from a team’s contributions. In both settings, we explore whether informing participants that group members’ identities will be disclosed at the end of the experiment leads to higher contributions to the public good. Non-parametric statistics indicate that when donations are costly for the participants, the announcement of subsequent identity disclosure results in significantly higher contributions in the second half of the repeated public good game. In contrast, revealing identities in settings with costless donations reduces contributions to the public good significantly. The regression results indicate that conditional cooperators might be one subgroup driving these results. Full article

Each year, millions of middle school graduates in China take a standardized test and compete for high school positions. Unlike other cities, Guangzhou still uses the immediate acceptance mechanism but implements a policy that students in the high-scoring group receive their allocations before those in the low-scoring group. In this paper, we study a class of the Guangzhou mechanisms, including the immediate acceptance (IA) and the serial dictatorship (SD) mechanism. We show that, if a collection of groups is refined by splitting its groups into a larger number of smaller subgroups, then the Guangzhou mechanism will perform more stably and less manipulable than before. This result provides a tool for policy makers to improve the allocation outcome of the IA mechanism under homogeneous priorities and justifies the use of a high-scoring student protection policy in Guangzhou’s high school admission. Full article

In this paper, we analyze the long run dynamics of a multi-agent game played on a one-dimensional lattice with periodic boundary conditions, i.e., a ring. Agents repeatedly play a 2 × 2 coordination game with neighbors where the payoff dominant action and the risk dominant action are distinct. Necessary and sufficient conditions for both the actions to be the unique long run equilibrium are provided. The result is obtained through the application of the radius and modified coradius technique. Full article