nep-gth New Economics Papers
on Game Theory
Issue of 2019‒09‒09
twenty-one papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Global Games With Strategic Complements and Substitutes By Eric J. Hoffmann; Tarun Sabarwal
  2. The Attack and Defense Games By Roman M. Sheremeta
  3. On the Predictive Power of Theories of One-Shot Play By Philipp Külpmann; Christoph Kuzmics
  4. Prudent Rationalizability in Generalized Extensive-Form Games with Unawareness By Burkhard C. Schipper; Martin Meier; Aviad Heifetz
  5. Distributional Preferences Explain Individual Behavior Across Games and Time By Morten Hedegaard; Rudolf Kerschbamer; Daniel Müler; Jean-Robert Tyran
  6. On the Existence of Equilibrium in Bayesian Games Without Complementarities By Idione Meneghel; Rabee Tourky
  7. Value-Capture in the Face of Known and Unknown Unknowns By Burkhard C. Schipper; Kevin Bryan; Michael Ryall
  8. Compliance with socially responsible norms of behavior: reputation vs. conformity By Virginia Cecchini Manara; Lorenzo Sacconi
  9. Voting on Sanctioning Institutions in Open and Closed Communities: Experimental Evidence By Ramón Cobo-Reyes; Gabriel Katz; Thomas Markussen; Simone Meraglia
  10. Preferences for efficiency, rather than preferences for morality, drive cooperation in the one-shot Stag-Hunt Game By Valerio Capararo; Ismael Rodriguez-Lara; Maria J. Ruiz Martos
  11. Expectations of reciprocity when competitors share information: Experimental evidence By Ganglmair, Bernhard; Holcomb, Alex; Myung, Noah
  12. Governance, Reforms and Crowding out Risk in Italian CCBs By Virginia Cecchini Manara; Lorenzo Sacconi
  13. Realistic versus Rational Secret Sharing By Yvo Desmedt; Arkadii Slinko
  14. MFGs for partially reversible investment By Haoyang Cao; Xin Guo; Joon Seok Lee
  15. The interdependence of domestic and international success: the case of the UEFA Champions League By Moreno-Ternero, Juan D.; Weber, Shlomo
  16. Institutions, Frames, and Social Contract Reasoning By Virginia Cecchini Manara; Lorenzo Sacconi
  17. Strategic Interdependence in Political Movements and Countermovements By Anselm Hager; Lukas Hensel; Johannes Hermle; Christopher Roth
  18. The economics of minority language use: theory and empirical evidence for a language game model By Stefan Sperlich; Jose-Ramon Uriarte
  19. A Theory of Power Wars By Herrera, Helios; Morelli, Massimo; Nunnari, Salvatore
  20. On the Notions of Equilibria for Time-Inconsistent Stopping Problems in Continuous Time By Erhan Bayraktar; Jingjie Zhang; Zhou Zhou
  21. Delegation Using Forward Induction By Swagata Bhattacharjee

  1. By: Eric J. Hoffmann (Department of Economics, The University of Kansas); Tarun Sabarwal (Department of Economics, University of Kansas)
    Abstract: We extend the global games method to the class of finite player, finite action games that includes games with strategic complements, games with strategic substitutes, and arbitrary combinations of the two. Our result is based on common order properties present in both strategic complements and substitutes, the notion of p-dominance, and the use of dominance solvability as the solution concept. In addition to being closer to the original arguments in Carlsson and van Damme (1993), our approach requires fewer additional assumptions. In particular, we require only one dominance region, and no assumptions on state monotonicity, or aggregative structure, or overlapping dominance regions. As expected, the p-dominance condition becomes more restrictive as the number of players increases. In cases where the probabilistic burden in belief formation may be reduced, the p-dominance condition may be relaxed as well. We present examples that are not covered by existing results.
    Keywords: Global games, Strategic complements, Strategic substitutes, Monotone games, Equilibrium selection
    JEL: C70 C72
    Date: 2019–08
  2. By: Roman M. Sheremeta (Weatherhead School of Management, Case Western Reserve University and Economic Science Institute, Chapman University)
    Abstract: The attack and defense game is a game in which an attacker (a group of attackers) has an incentive to revise the status quo and a defender (a group of defenders) wants to protect it. The asymmetry in objectives creates incompatible interests and results in a mixed-strategy Nash equilibrium. However, this equilibrium could be heavily impacted by behavioral considerations.
    Keywords: contest, experiment, attack, defense
    JEL: C72 C91 D72 D74
    Date: 2019
  3. By: Philipp Külpmann (University of Vienna, Austria); Christoph Kuzmics (University of Graz, Austria)
    Abstract: We propose a novel challenge for assessing the predictive power of a theory of one shotplay in games (subjects playing a game exactly once): we test the predictive power of theories in situations for which we do not (yet) have any data. To do so, we consider a variety of such theories and fix their parameter estimates from the recent large scale meta-analysis of Wright and Leyton-Brown (2017). We then compare the predictive power of these theories, measured in terms of log-likelihood, for a series of symmetric hawk-dove games played in the lab. We find that even for such a narrow class of games, no theory is uniformly better than all others across all treatments. Furthermore, the theory that provides the highest overall log-likelihood for our data is Nash equilibrium with risk aversion, with an estimated risk aversion parameter taken from Hey and Orme (1994) and its replication in Harrison and Rutström (2009). In particular, it significantly beats the two theories (based on quantal level k and cognitive hierarchy models) which performed best in Wright and Leyton-Brown’s (2017) standard out-of-sample prediction task.
    Keywords: Hawk-dove games; Testing theories; One-shot play; Risk aversion; Nash equilibrium, Quantal response equilibria; Level-k theory; Cognitive hierarchy theory
    JEL: C72 C91
    Date: 2019–09
  4. By: Burkhard C. Schipper; Martin Meier; Aviad Heifetz (Department of Economics, University of California Davis)
    Abstract: We define a cautious version of extensive-form rationalizability for generalized extensive-form games with unawareness that we call prudent rationalizability. It is an extensive-form analogue of iterated admissibility. In each round of the procedure, for each tree and each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. We demonstrate the applicability of prudent rationalizability. In games of disclosure of verifiable information, we show that prudent rationalizability yields unraveling under full awareness but unraveling might fail under unawareness. We compare prudent rationalizability to extensive-form rationalizability. We show that prudent rationalizability may not refine extensive-form rationalizability strategies but conjecture that the paths induced by prudent rationalizable strategy profiles (weakly) refine the set of paths induced by extensive-form rationalizable strategies.
    Keywords: Caution, extensive-form rationalizability, unawareness, disclosure, verifiable information, persuasion games, iterated admissibility, common strong cautious belief in rationality
    JEL: C72 D83
    Date: 2019–08–28
  5. By: Morten Hedegaard (Department of Economics, University of Copenhagen, Denmark); Rudolf Kerschbamer (University of Innsbruck, Austria); Daniel Müler (University of Innsbruck, Austria); Jean-Robert Tyran (Department of Economics, University of Copenhagen, Denmark)
    Abstract: We use a large and heterogeneous sample of the Danish population to investigate the importance of distributional preferences for behavior in a public good game and a trust game. We find robust evidence for the significant explanatory power of distributional preferences. In fact, compared to twenty-one covariates, distributional preferences turn out to be the single most important predictor of behavior. Specifically, subjects who reveal benevolence in the domain of advantageous inequality contribute more to the public good and are more likely to pick the trustworthy action in the trust game than other subjects. Since the experiments were spread out more than one year, our results suggest that there is a component of distributional preferences that is stable across games and over time.
    Keywords: Distributional preferences, social preferences, Equality-Equivalence Test, representative online experiment, trust game, public goods game, dictator game
    JEL: C72 C91 D64
    Date: 2019–05–15
  6. By: Idione Meneghel (Australian National University College of Business and Economics); Rabee Tourky (Australian National University College of Business and Economics)
    Abstract: In a recent paper, Reny (2011) generalized the results of Athey (2001) and McAdams (2003) on the existence of monotone strategy equilibrium in Bayesian games. Though the generalization is subtle, Reny introduces far-reaching new techniques applying the fixed point theorem of Eilenberg and Montgomery (1946, Theorem 5). This is done by showing that with atomless type spaces the set of monotone functions is an absolute retract and when the values of the best response correspondence are non-empty sub-semilattices of monotone functions, they too are absolute retracts. In this paper, we provide an extensive generalization of Reny (2011), McAdams (2003), and Athey (2001). We study the problem of existence of Bayesian equilibrium in pure strategies for a given partially ordered compact subset of strategies. The ordering need not be a semilattice and these strategies need not be monotone. The main innovation is the interplay between the homotopy structures of the order complexes that are the subject of the celebrated work of Quillen (1978), and the hulling of partially ordered sets, an innovation that extends the properties of Reny’s semilattices to the non-lattice setting. We then describe some auctions that illustrate how this framework can be applied to generalize the existing results and extend the class of models for which we can establish existence of equilibrium. As with Reny (2011), our proof utilizes the fixed point theorem in Eilenberg and Montgomery (1946).
    Keywords: Bayesian games, Monotone strategies, Pure-strategy equilibrium, Auctions
    Date: 2019–08
  7. By: Burkhard C. Schipper; Kevin Bryan; Michael Ryall (Department of Economics, University of California Davis)
    Abstract: A large theoretical literature on value capture following Brandenburger and Stuart (1996) uses cooperative games under complete information to study how and why firms earn supernormal profits. However, firms often have different information, beliefs, or creative foresight. We extend value capture theory to incomplete information (``known unknowns'') or unawareness (``unknown unknowns''), and illustrate some conceptual issues with that extension. Using the case study of Cirque du Soleil, we show how an entrepreneurial firm can profit even when it does not contribute materially to value creation.
    Keywords: cooperative games, unawareness, incomplete information, coarse core, business strategy, value-capture theory
    JEL: D21 D83 C71
    Date: 2019–08–28
  8. By: Virginia Cecchini Manara (University of Trento); Lorenzo Sacconi (University of Milan)
    Abstract: The Social Responsibility of Business usually involves self-regulation, which entails spontaneous compliance with social norms or standards that are not imposed by hard law. In this paper we discuss the mechanisms that lead economic agents to comply with socially responsible norms that are not legally enforced, and do not coincide with profit, or self-interest, maximization. Companies exist because individuals need to cooperate and some institutions can facilitate cooperation, but at the same time these institutions may turn into places where unfair distributions are amplified and cooperative behaviours and motivations disrupted. The agents who decide to organize themselves into firms are usually motivated by the need to earn some benefit from mutual cooperation: since they have limited knowledge and bounded rationality, team production can highly improve their results. Therefore the main motivation to enter an organization is to gain from cooperation; but this also brings problems of how to divide the surplus that is generated and we find conflicts on the attribution of benefits among stakeholders, with a particular problem of abuse of authority by those who hold power. One of the drivers of socially responsible behaviour is the quest for reputation, which in turn induces a cooperative response from the stakeholders. This can be described in game-theoretical terms with a repeated Trust Game between a trustor (the stakeholder) and a trustee (the management of the firm). The problem with reputation is that it is compatible with multiple equilibria, included the one in which stakeholders always trust the firm, and the firm often abuses this trust. This leads to consider an alternative mechanism for norm compliance: conformity and reciprocity that derive from an impartial agreement among stakeholders. The present work analyses in depth the role of an agreement on cognitions and motivations, grounding on insights from psychology, game theory and experimental findings.
    Keywords: corporate culture, CSR, social contract, agreement, trust game
    JEL: C72 M14 L14 D91
    Date: 2019–08
  9. By: Ramón Cobo-Reyes (Department of Economics, American University of Sharjah); Gabriel Katz (Department of Politics, University of Exeter); Thomas Markussen (Department of Economics, University of Copenhagen, Denmark); Simone Meraglia (Department of Politics, University of Exeter)
    Abstract: We experimentally analyze the eect of endogenous group formation on the type of sanctioning institutions emerging in a society. We allocate subjects to one of two groups. Subjects play a repeated public goods game and vote on the sanctioning system (formal or informal) to be implemented in their group. We compare this environment to one in which subjects are allowed to (i) vote on the sanctioning system and (ii) move between groups. We find that the possibility of moving between groups leads to a larger proportion of subjects voting for formal sanctions. This result is mainly driven by subjects in groups with relatively high initial levels of contribution to the public good, who are more likely to vote for informal sanctions when groups are closed than when they are open.
    Keywords: Sanctions, Cooperation, Group Formation, Voting, Experiment
    JEL: C73 C91 C92 D72 H41
    Date: 2019–05–23
  10. By: Valerio Capararo (Department of Economics, Middlesex University.); Ismael Rodriguez-Lara (Department of Economic Theory and Economic History, University of Granada.); Maria J. Ruiz Martos (Department of Economic Theory and Economic History, University of Granada.)
    Abstract: Recent work highlights that cooperation in the one-shot Prisoner’s dilemma (PD) is primarily driven by moral preferences for doing the right thing, rather than social preferences for equity or efficiency. By contrast, little is known on what motivates cooperation in the Stag-Hunt Game (SHG). Cooperation in the SHG fundamentally differs from cooperation in the PD in that it is not costly, but risky: players have no temptation to deviate from the cooperative outcome, but cooperation only pays off if the other player cooperates. Here, we provide data from a large (N=436), pre-registered, experiment. Contrary to what has been observed for the PD, we find that SHG cooperation is primarily driven by preferences for efficiency, rather than preferences for doing the right thing.
    Keywords: morality, cooperation, efficiency, risky choices, stag-hunt game.
    Date: 2019–08–09
  11. By: Ganglmair, Bernhard; Holcomb, Alex; Myung, Noah
    Abstract: Informal exchange of information among competitors has been well-documented in a variety of industries, and one's expectation of reciprocity shown to be a key determinant. We use an indeterminate horizon centipede game to establish a feedback loop in the laboratory and show that an individual's beliefs about the recipient's intentions to reciprocate matter more than a recipient's ability to do so. This implies that reducing strategic uncertainty about a competitor's behavior has a stronger effect on information ows than reducing environmental uncertainty (about the competitor's ability). We further show results on the formation of beliefs and discuss managerial implications.
    Keywords: knowledge diffusion,information sharing,reciprocity,conversation,experimental economics,centipede game
    JEL: O33 D8 C72 C91
    Date: 2019
  12. By: Virginia Cecchini Manara (University of Trento); Lorenzo Sacconi (University of Milan)
    Abstract: The Italian reform of Cooperative Banks (legislative decree 18/2016 converted into law 49/2016) was created to address the main structural and economic difficulties that the Italian cooperative credit sector is facing. This work intends to evaluate the impact of the reform and to warn against the risk that it could intervene negatively on the fundamental values of cooperative credit (mutuality, localism and solidarity within the community to which it belongs), without taking into account the non-profit multi-stakeholder nature and of the cooperative banks (BCC: Banche di Credito Cooperativo). In the proposed model, the study of the non-material motivational component of the subjects, which in this work is identified in conformity preferences, assumes a central importance. The emergence of “virtuous†behavior in this context can be explained as the equilibrium outcome of a game in which players do not act solely pursuing self-interest, but also and above all as individuals belonging to the same community that shares ideal principles on the equitable sharing of wealth. However, because the intrinsic motivations are fundamental but also fragile, our study of the effects of the reform mainly focused on the risk that such intervention might alter or even oust the intrinsic motivations of the subjects (crowding-out effect), threatening the stability of the motivational system that guarantees the existence of the BCCs. The purpose of this work is to investigate whether a large-scale legislative intervention, such as the recent reform of the BCC, could end up altering the essential characteristics of the cooperative credit system, putting its integrity and uniqueness at risk. Starting from a descriptive model of the BCCs in a context of interaction among different stakeholders, characterized by motivations of conformity to an ideal (conformity preferences - Grimalda and Sacconi, 2005), various ways of external intervention are hypothesized and the risk of crowding out of the intrinsic motivations of individuals (Frey, 1997) is analyzed.
    Keywords: cooperative banks, institutional diversity, fairness, psychological games, intrinsic motivations, corporate governance
    JEL: C72 D63 G21 G28
    Date: 2019–08
  13. By: Yvo Desmedt; Arkadii Slinko
    Abstract: The study of Rational Secret Sharing initiated by Halpern and Teague regards the reconstruction of the secret in secret sharing as a game. It was shown that participants (parties) may refuse to reveal their shares and so the reconstruction may fail. Moreover, a refusal to reveal the share may be a dominant strategy of a party. In this paper we consider secret sharing as a sub-action or subgame of a larger action/game where the secret opens a possibility of consumption of a certain common good. We claim that utilities of participants will be dependent on the nature of this common good. In particular, Halpern and Teague scenario corresponds to a rivalrous and excludable common good. We consider the case when this common good is non-rivalrous and non-excludable and find many natural Nash equilibria. We list several applications of secret sharing to demonstrate our claim and give corresponding scenarios. In such circumstances the secret sharing scheme facilitates a power sharing agreement in the society. We also state that non-reconstruction may be beneficial for this society and give several examples.
    Date: 2019–08
  14. By: Haoyang Cao; Xin Guo; Joon Seok Lee
    Abstract: This paper analyzes a class of MFGs with singular controls motivated from the partially reversible problem. It establishes the existence of the solution when controls are of bounded velocity, solves explicitly the game when controls are of finite variation, and presents sensitivity analysis to compare the single-player game with the MFG. Our analysis shows that MFGs, when appropriately formulated, can demonstrate genuine game effects even without heterogeneity among players and additional common noise.
    Date: 2019–08
  15. By: Moreno-Ternero, Juan D.; Weber, Shlomo
    Abstract: This article explores interdependence of domestic and international success in sports where leading clubs enter international competitions while competing in their domestic leagues. Taking as starting point the success of Spanish football teams in the UEFA Champions League during the 2008-2018 decade, we provide a stylized game-theoretical model in which national competitions determine the level of competitive balance therein. We rationalize the hypothesis that intermediate levels of competitiveness within domestic competitions are instrumental in achieving international success.
    Keywords: competitive balance; domestic competitions; international competitions; Nash equilibrium; UEFA Champions League
    Date: 2019–08
  16. By: Virginia Cecchini Manara (University of Trento); Lorenzo Sacconi (University of Milan)
    Abstract: This work aims at filling a gap in the cognitive representation of institutions, starting from Aoki’s account of institutions as equilibria in a game- theoretical framework. We propose a formal model to explain what happens when different players hold different representations of the game they are playing. In particular, we assume that agents do not know all the feasible strategies they can play, because they have bounded rationality; grounding on the works by Johnson-Laird and his coauthors, we suggest that individuals use parsimonious mental models that make as little as possible explicit to represent the game they are playing, because of their limited capacity of working memory and attention. Second, we rely on Bacharach’s variable frame theory: agents transform the objective game into a framed game, where strategies are “labeled†in some sense. In such a context, we argue that a social contract – given its prescriptive and universalizable meaning – may provide a shared mental model, accepted by all players, that allows agents to select a joint plan of action corresponding to an efficient and fair distribution.
    Keywords: social institutions, shared beliefs, mental models, framing, social contract
    JEL: B52 C7 D02 D83
    Date: 2019–08
  17. By: Anselm Hager; Lukas Hensel; Johannes Hermle; Christopher Roth
    Abstract: We study participation in right-wing rallies and counterrallies in Germany to examine strategic interactions in political movements. In the leadup to two right-wing rallies, we exogenously shift potential participants’ beliefs about the turnout at the right-wing rally and left-wing counterrally, and then measure activists’ intentions to protest. For right-wing activists, own participation and participation of peers exhibit strategic substitutability. For left-wing activists, own participation and participation of peers are strategic complements. Both groups do not, however, react to changes in competitor effort. Our evidence highlights substantial heterogeneity in the nature of strategic interactions in political movements.
    Keywords: political rallies, field experiment, strategic behavior, beliefs
    JEL: D74 D80 P00
    Date: 2019
  18. By: Stefan Sperlich; Jose-Ramon Uriarte
    Abstract: Language and cultural diversity is a fundamental aspect of the present world. We study three modern multilingual societies -- the Basque Country, Ireland and Wales -- which are endowed with two, linguistically distant, official languages: $A$, spoken by all individuals, and $B$, spoken by a bilingual minority. In the three cases it is observed a decay in the use of minoritarian $B$, a sign of diversity loss. However, for the "Council of Europe" the key factor to avoid the shift of $B$ is its use in all domains. Thus, we investigate the language choices of the bilinguals by means of an evolutionary game theoretic model. We show that the language population dynamics has reached an evolutionary stable equilibrium where a fraction of bilinguals have shifted to speak $A$. Thus, this equilibrium captures the decline in the use of $B$. To test the theory we build empirical models that predict the use of $B$ for each proportion of bilinguals. We show that model-based predictions fit very well the observed use of Basque, Irish, and Welsh.
    Date: 2019–08
  19. By: Herrera, Helios; Morelli, Massimo; Nunnari, Salvatore
    Abstract: This paper provides a theory of how war onset and war duration depend on the initial distribution of power when conflict triggers a reallocation of power but the loser is not eliminated. In the model, players take into account not only the expected consequences of war on the current distribution of resources, but also its expected consequences on the future distribution of military and political power. We highlight three main results: the key driver of war, in both the static and the dynamic game, is the mismatch between military and political power; dynamic incentives usually amplify static incentives, leading forward-looking players to be more aggressive; and a war is more likely to last for longer if political power is initially more unbalanced than military power and the politically under-represented player is militarily advantaged.
    Keywords: Balance of powers; War Duration
    Date: 2019–08
  20. By: Erhan Bayraktar; Jingjie Zhang; Zhou Zhou
    Abstract: A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{weak equilibrium} respectively, a strong equilibrium captures the idea of subgame perfect Nash equilibrium more accurately. When the state process is a continuous-time Markov chain and the discount function is log sub-additive, we show that an optimal mild equilibrium is always a strong equilibrium. Moreover, we provide a new iteration method that can directly construct an optimal mild equilibrium and thus also prove its existence.
    Date: 2019–09
  21. By: Swagata Bhattacharjee (Ashoka University)
    Abstract: This paper explores a potentially important role of delegation: as a signal to sustain cooperation in coordination games. I consider a static principal-agent model with two tasks, one of which requires cooperation between the principal and the agent. If there is asymmetric information about the agent's type, the principal with a private belief that the agent is a good type can delegate the first task as a signal of his private belief. This equilibrium is supported by the forward induction argument. I conduct laboratory experiments to test these theoretical predictions and to examine the role of information in equilibrium selection. I find that delegation is used only sometimes to facilitate cooperation; however, when the subjects have information about past sessions, there is a statistically significant increase in the use of delegation. This evidence suggests that information matters in equilibrium selection in Bayesian games.
    Keywords: Delegation, Forward Induction, Lab Experiment, Information
    Date: 2019–08

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