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on Game Theory |
| By: | Orlova, Olena (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We consider network games in which players simultaneously form partnerships and choose actions. Players are heterogeneous with respect to their action preferences. We characterize pairwise Nash equilibria for a large class of games, including coordination and anti-coordination games, varying the strength of action preferences and the size of the linking cost. We find that, despite the symmetry and simplicity of the setting, quite irregular network structures can arise in equilibrium, implying that heterogeneity in players' action preferences may already explain a large part of observed irregularity in endogenously formed networks. |
| Keywords: | network games, strategic network formation, preference heterogeneity, efficiency |
| Date: | 2021–12–22 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:659&r= |
| By: | Pierpaolo Battigalli; Nicolò Generoso |
| Abstract: | We propose that the mathematical representation of situations of strategic interactions, i.e., of games, should separate the description of the rules of the game from the description of players’ personal traits. Yet, we note that the standard extensive-form partitional representation of information in sequential games does not comply with this separation principle. We offer an alternative representation that extends to all (finite) sequential games the approach adopted in the theory of repeated games with imperfect monitoring, that is, we describe the flow of information accruing to players rather than the stock of information retained by players, as encoded in information partitions. Mnemonic abilities can be represented independently of games. Assuming that players have perfect memory, our flow representation gives rise to information partitions satisfying perfect recall. Different combinations of rules about information flows and of players mnemonic abilities may give rise to the same information partition . All extensive-form representations with information partitions, including those featuring absentmindedness, can be generated by some such combinations. |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:678&r= |
| By: | Pangallo, Marco; Heinrich, Torsten; Jang, Yoojin; Scott, Alex; Tarbush, Bassel; Wiese, Samuel; Mungo, Luca |
| Abstract: | We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence—the order in which players update their actions—is essentially irrelevant in determining whether the dynamic converges to a Nash equilibrium in certain classes of games (e.g. in potential games) but, when evaluated across all possible games, convergence to equilibrium depends on the playing sequence in an extreme way. Our main asymptotic result shows that the best-response dynamic converges to a pure Nash equilibrium in a vanishingly small fraction of all (large) games when players take turns according to a fixed cyclic order. By contrast, when the playing sequence is random, the dynamic converges to a pure Nash equilibrium if one exists in almost all (large) games. |
| Keywords: | Best-response dynamics, equilibrium convergence, random games |
| JEL: | C62 C72 C73 D83 |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:amz:wpaper:2021-23&r= |
| By: | Masaki Aoyagi; Guillaume Frechette; Sevgi Yuksel |
| Abstract: | This paper uses a laboratory experiment to study beliefs and their relationship to action and strategy choices in finitely and indefinitely repeated prisoners' dilemma games. We find subjects' beliefs about the other player's action are accurate despite some systematic deviations corresponding to early pessimism in the indefinitely repeated game and late optimism in the finitely repeated game. The data reveals a close link between beliefs and actions that differs between the two games. In particular, the same history of play leads to different beliefs, and the same belief leads to different action choices in each game. Moreover, we find beliefs anticipate the evolution of behavior within a supergame, changing in response to the history of play (in both games) and the number of rounds played (in the finitely repeated game). We then use the subjects' beliefs over actions in each round to identify their beliefs over supergame strategies played by the other player. We find these beliefs correctly capture the different classes of strategies used in each game. Importantly, subjects using different strategies have different beliefs, and for the most part, strategies are subjectively rational given beliefs. The results also suggest subjects tend to overestimate the likelihood that others use the same strategy as them, while underestimating the likelihood that others use less cooperative strategies. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1119r&r= |
| By: | Raouf Boucekkine (Rennes School of Business); Giorgio Fabbri (Univ. Grenoble Alpes, CNRS, INRA, Grenoble INP, GAEL, 38000 Grenoble, France.); Salvatore Federico (Università degli Studi di Genova, Dipartimento di Economia.); Fausto Gozzi (Dipartimento di Economia e Finanza, LUISS Guido Carli, Roma.) |
| Abstract: | This work targets the class of spatiotemporal problems with free riding under natural (pollution, epidemics...etc) diffusion and spatial externalities. Such a class brings to study a family of differential games in continuous time and space. In the fundamental pollution free riding problem we develop a strategy to solve completely the associated game contributing to the associated debate on environmental federalism. We depart from the preexisting literature in several respects. First, instead of assuming ad hoc pollution diffusion schemes across space, we consider a realistic spatiotemporal law of motion for pollution (diffusion and advection). Second, we tackle spatiotemporal non-cooperative (and cooperative) differential games instead of static games in the related literature. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. Third, we allow for a rich set of geographic heterogeneities across states while the literature assumes identical states. We solve analytically the induced non-cooperative differential game under decentralization and fully characterize the resulting long-term spatial distributions. In particular, we prove that there exist a Perfect Markov Equilibrium, unique among the class of the a‑ne feedbacks. We further provide with full exploration of the free riding problem, reflected in the so-called border effects. Finally, we explore how geographic discrepancies (the most elementary being the asymmetry of players) affect the shape of the border effects. We check in particular that our model is consistent with the set of stylized facts put forward by the related empirical literature. |
| Keywords: | Spatial externalities, spatial diffusion, differential games in continuous time and space, infinite dimensional optimal control problems, environmental federalism |
| JEL: | Q53 R12 O13 C72 C61 O44 |
| Date: | 2021–11–18 |
| URL: | http://d.repec.org/n?u=RePEc:ctl:louvir:2021028&r= |
| By: | Shin Kobayashi (Graduate School of Economics, Waseda University, 1-6-1 Nishiwaseda Shinjuku-ku, Tokyo 169-8050, Japan.) |
| Abstract: | We examine the relationship between the Shapley value and the excess. Defining the excess of player i by summing up the excesses of all the coalitions to which i belongs, we introduce a condition equal excess. Using this condition, we prove that the Shapley value is characterized as a value satisfying the equal excess with respect to a reasonable weight function. This implies that the Shapley value attains the greatest benefits of the least advantaged players. |
| Keywords: | Shapley value; Equal excess; Difference principle; Least square values |
| JEL: | C71 |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:wap:wpaper:2120&r= |
| By: | Federico Belotti (CEIS & DEF, University of Rome "Tor Vergata"); Eloisa Campioni (CEIS & DEF, University of Rome "Tor Vergata"); Vittorio Larocca (Luiss Guido Carli); Francesca Marazzi (CEIS, University of Rome "Tor Vergata"); Luca Panaccione (University of Rome "La Sapienza"); Andrea Piano Mortari (CEIS, University of Rome "Tor Vergata") |
| Abstract: | We run a laboratory experiment to investigate how the size of the group affects coordination in a bank-run game played repeatedly by participants facing different fellow depositors. For comparability purposes, we keep the coordination tightness constant across different sizes. Participants exhibit an adaptive behavior, since the main drivers of their decisions to withdraw are: previous-round outcomes and own initial choice. Moreover, they mainly adopt the best response to previous-round feedback. However, a sizeable share of participants adopts the opposite mode of behavior, that we refer to as experimentation. The analysis of the determinants of experimentation suggest that subjects adopt this behavior when the probability to lead the group toward the efficient outcome is higher. Finally, our analysis shows that the size of the bank has a significant effect on participants’ decisions, since they withdraw more and experiment less in large banks. |
| Keywords: | Coordination Games, Experimental Studies, Bank Runs |
| JEL: | C70 C92 D80 G21 |
| Date: | 2021–12–13 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:529&r= |
| By: | Anwesha Banerjee |
| Abstract: | This paper presents a model of private provision of a public good where individuals in a group have altruistic preferences and care about the private and public good consumption of the other members of the group. I show that increasing the level of altruism increases the Nash level of the public good, demonstrating that caring about others improves public good provision. I then compare the Nash level of the public good to the benchmark level of provision by a social planner who aggregates the preferences of the group. I ï¬ nd that if there are non-contributors to the public good in a Nash equilibrium, income inequality can cause over-provision of the public good as compared to the planner’s benchmark. Over-provision can occur because the poorest in the society do not contribute and the richer individuals contribute to the public good as a way to improve the welfare of the poor. These results indicate that public goods cannot substitute the role of government income transfers to the poor even when individuals are altruistic if the distribution of incomes is highly unequal. |
| Keywords: | Public goods, Altruism, Private transfers. |
| JEL: | C72 H41 D64 |
| Date: | 2021–06 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2021-08&r= |
| By: | Xiaohui Bei; Xinhang Lu; Warut Suksompong |
| Abstract: | The classic cake cutting problem concerns the fair allocation of a heterogeneous resource among interested agents. In this paper, we study a public goods variant of the problem, where instead of competing with one another for the cake, the agents all share the same subset of the cake which must be chosen subject to a length constraint. We focus on the design of truthful and fair mechanisms in the presence of strategic agents who have piecewise uniform utilities over the cake. On the one hand, we show that the leximin solution is truthful and moreover maximizes an egalitarian welfare measure among all truthful and position oblivious mechanisms. On the other hand, we demonstrate that the maximum Nash welfare solution is truthful for two agents but not in general. Our results assume that mechanisms can block each agent from accessing parts that the agent does not claim to desire; we provide an impossibility result when blocking is not allowed. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.05632&r= |
| By: | Biljana Meiske |
| Abstract: | This paper studies the consequences of productivity shocks on conflict behavior in the presence of loss aversion. In a first step, I incorporate expectation based loss preferences `a la KË oszegi and Rabin (2006, 2007) into a Hirshleifer-Skaperdas conflict game and show that negative productivity shocks entail larger conflict investments if agents are loss averse (and smaller investments if agents are gain-seeking); the reverse holds in case of a positive productivity shock. In a second step, a lab experiment (N=496) was conducted with participants playing repeated guns-and-butter conflict game under changing productivity regimes. The experimental results reveal that while negative productivity shocks (channeled through loss aversion) have the predicted effects, positive productivity shocks lead to the predicted increase in conflict investment among gain-seeking, but fail to reduce conflict investment among loss-averse participants. Furthermore, absent any changes in productivity level, conflict investments are shown to increase in the level of loss aversion. |
| Keywords: | conflict rent-seeking loss aversion reference dependence productivity shocks |
| JEL: | D91 C92 D72 D74 |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2021-18&r= |
| By: | Pierpaolo Battigalli; Emiliano Catonini; Julien Manili |
| Abstract: | Strategic reasoning in sequential games rests on figuring out how (co)players would react to information about past play, which in turn depends on how players update or revise their beliefs. Several notions of belief systems have been used to represent and discipline how players’ beliefs change as they obtain new information. Such notions differ and can be nested according to the imposed consistency restrictions relating beliefs at different information sets. The minimal restriction requires that beliefs about others change from one information set to a following, more informative one in compliance with the chain rule, i.e., by standard updating whenever possible. On top of this, more demanding restrictions require that beliefs about co-players depend only on information about them, not on own past moves. Even stronger restrictions require that players update, or revise their beliefs as if they could notionally condition on any nonempty event about co-players’ behavior in compliance with the chain rule. We analyze restrictions on belief change, providing characterizations and interpretations in terms of introspection and cognitive rationality. We then argue that these differences between consistency restrictions do not affect the behavioral implications of strategic reasoning in games. |
| Keywords: | Sequential games, chain rule, partial introspection, rational planning, rationalizability. JEL Codes: C72, C73, D83. |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:679&r= |
| By: | Kai A. Konrad; Florian Morath |
| Abstract: | We study collective action under adverse incentives: each member of the group has a given budget (‘use-it-or-lose-it’) that is his private information and that can be used for contributions to make the group win a prize and for internal …fights about this very prize. Even in the face of such rivalry in resource use, the group often succeeds to overcome the collective action problem in non-cooperative equilibrium. One type of equilibrium has group members who both contribute, the other type has volunteers who make full stand-alone contributions. Both types of equilibrium exist for larger and partially overlapping parameter ranges. |
| Keywords: | Blotto budgets; intra-group conflict; threshold public good; collective action; all-pay auction; incomplete information |
| JEL: | D72 D74 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2021-13&r= |
| By: | Wayne Geerling (Monash University); Kristofer Nagy (Monash University); Elaine Rhee (University of Arizona); Jadrian Wooten (Penn State University) |
| Abstract: | Economic educators have been teaching with pop culture for decades, but until recently the focus was on English-based media. In this paper, we build on the work of Wooten al. (2021b), who showed how K-pop can be integrated into the principles-level curriculum. We develop three teaching guides that can be used to teach aspects of behavioral economics, game theory and indifference curve analysis – topics which are taught at the end of most principles-level courses but are also standalone upper level courses. The three artists chosen – BTS, BLACKPINK and TWICE – have huge global followings. We hope this paper will contribute to the library of diverse and inclusive teaching resources while helping to address the deficit of resources available to instructors of upper level courses. |
| Keywords: | Inclusive teaching, media, music, teaching economics, game theory |
| JEL: | A20 A21 |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:mos:moswps:2021-18&r= |
| By: | Mikhail Anufriev; Kirill Borissov; Mikhail Pakhnin |
| Abstract: | We study a model of social learning in networks where the dynamics of beliefs are driven by conversations of dissonance-minimizing agents. Given their current beliefs, agents make statements, tune them to the statements of their associates, and then revise their beliefs. We characterize the long-run beliefs in a society, provide the necessary and sufficient conditions for a society to reach a consensus, and show that agents’ social influences (weights on the consensus belief) are decreasing in their dissonance sensitivities. Comparing the outcomes of two models, with and without conversation, we show that conversation leads to a redistribution of social influences in favor of agents with higher self-confidence. Finally, we provide analytical insights for the model where agents minimize dissonance by revising both beliefs and network, and show that an endogenous change of network may prevent a society from reaching a consensus. |
| Keywords: | social networks, DeGroot learning, social influence, dissonance minimization, conversation |
| JEL: | D83 D85 D91 Z13 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9433&r= |
| By: | Georgios Piliouras; Ryann Sim; Stratis Skoulakis |
| Abstract: | In this paper we solve the problem of no-regret learning in general games. Specifically, we provide a simple and practical algorithm that achieves constant regret with fixed step-sizes. The cumulative regret of our algorithm provably decreases linearly as the step-size increases. Our findings depart from the prevailing paradigm that vanishing step-sizes are a prerequisite for low regret as championed by all state-of-the-art methods to date. We shift away from this paradigm by defining a novel algorithm that we call Clairvoyant Multiplicative Weights Updates (CMWU). CMWU is Multiplicative Weights Updates (MWU) equipped with a mental model (jointly shared across all agents) about the state of the system in its next period. Each agent records its mixed strategy, i.e., its belief about what it expects to play in the next period, in this shared mental model which is internally updated using MWU without any changes to the real-world behavior up until it equilibrates, thus marking its consistency with the next day's real-world outcome. It is then and only then that agents take action in the real-world, effectively doing so with the ``full knowledge" of the state of the system on the next day, i.e., they are clairvoyant. CMWU effectively acts as MWU with one day look-ahead, achieving bounded regret. At a technical level, we establish that self-consistent mental models exist for any choice of step-sizes and provide bounds on the step-size under which their uniqueness and linear-time computation are guaranteed via contraction mapping arguments. Our arguments extend well beyond normal-form games with little effort. |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2111.14737&r= |
| By: | Michal Bauer; Jana Cahlíková; Julie Chytilová; Gérard Roland; TomᚠŽelinskı |
| Abstract: | This paper provides experimental evidence showing that members of a majority group systematically shift punishment on innocent members of an ethnic minority. We develop a new incentivized task, the Punishing the Scapegoat Game, to measure how injustice affecting a member of one’s own group shapes punishment of an unrelated bystander (“a scapegoat†). We manipulate the ethnic identity of the scapegoats and study interactions between the majority group and the Roma minority in Slovakia. We find that when no harm is done, there is no evidence of discrimination against the ethnic minority. In contrast, when a member of one’s own group is harmed, the punishment †passed†on innocent individuals more than doubles when they are from the minority, as compared to when they are from the dominant group. These results illuminate how individualized tensions can be transformed into a group conflict, dragging minorities into conflicts in a way that is completely unrelated to their behavior. |
| Keywords: | punishment, minority groups, inter-group conflict, discrimination, scapegoating, lab-in-field experiments |
| JEL: | C93 D74 D91 J15 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2021-11&r= |