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on Game Theory |
| By: | Kets, Willemien (University of Oxford) |
| Abstract: | A standard assumption in game theory is that players have an infinite depth of reasoning: they think about what others think and about what others think that othersthink, and so on, ad infinitum. However, in practice, players may have a finite depth of reasoning. For example, a player may reason about what other players think, but not about what others think he thinks. This paper proposes a class of type spaces that generalizes the type space formalism due to Harsanyi (1967) so that it can model players with an arbitrary depth of reasoning. I show that the type space formalism does not impose any restrictions on the belief hierarchies that can be modeled, thus generalizing the classic result of Mertens and Zamir (1985). However, there is no universal type space that contains all type spaces. |
| Date: | 2021–04–24 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:qt498&r= |
| By: | Ezzat Elokda; Andrea Censi; Saverio Bolognani |
| Abstract: | In this paper, we define a new class of dynamic games played in large populations of anonymous agents. The behavior of agents in these games depends on a time-homogeneous type and a time-varying state, which are private to each agent and characterize their available actions and motifs. We consider finite type, state, and action spaces. On the individual agent level, the state evolves in discrete-time as the agent participates in interactions, in which the state transitions are affected by the agent's individual action and the distribution of other agents' states and actions. On the societal level, we consider that the agents form a continuum of mass and that interactions occur either synchronously or asynchronously, and derive models for the evolution of the agents' state distribution. We characterize the stationary equilibrium as the solution concept in our games, which is a condition where all agents are playing their best response and the state distribution is stationary. At least one stationary equilibrium is guaranteed to exist in every dynamic population game. Our approach intersects with previous works on anonymous sequential games, mean-field games, and Markov decision evolutionary games, but it is novel in how we relate the dynamic setting to a classical, static population game setting. In particular, stationary equilibria can be reduced to standard Nash equilibria in classical population games. This simplifies the analysis of these games and inspires the formulation of an evolutionary model for the coupled dynamics of both the agents' actions and states. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.14662&r= |
| By: | Sergio Alessandro Castagnetti; Sebastiano Massaro; Eugenio Proto |
| Abstract: | We investigate the effect of anger on performance and strategic cooperative interactions. In a laboratory experiment, we induced anger in participants playing an indefinite repeated Prisoner's Dilemma game against each other, showing resulting declines in performance and individual profit. We assess the dynamics of strategic cooperative decisions and behaviors, revealing that anger-induced subjects used suboptimal strategies. We further describe the underpinning mechanism of automatic emotional regulation by analyzing participants' heart rate variability indexes. Finally, we extend our findings in an online experiment with an independent sample, increasing generalizability and helping explain how anger influences participants' ways of strategizing. Altogether, our contribution advances theoretical and practical implications regarding the impact of discrete emotions on strategic outcomes. |
| Keywords: | anger; behavioral strategy; heart rate variability; indefinite repeated Prisoner’s Dilemma; strategic cooperative interactions |
| JEL: | C7 C9 D9 |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2021_05&r= |
| By: | Aghadadashli, Hamid; Kirchsteiger, Georg; Legros, Patrick |
| Abstract: | The paper studies the effectiveness of communication in a two-player two-sided asymmetric information context. Both players choose simultaneously between two actions, with action L leading to a lower payoff for the co-player than action H. There are two types of players: D-types for whom L is dominant, and C-types for whom the optimal action is the same as the one chosen by the co-player, with both player choosing H providing the C-type a higher payoff than both players choosing L. Before the actions are chosen, each player can signal his/her intention to choose H. We consider three communication environments: No communication (NC), cheap talk (CT), and an environment with extrinsic communication costs (FC). For this game the range of equilibrium payoffs of both types is the same in NC and CT, while for C-types the equilibrium payoff is highest in FC due to the Spence mechanism (Spence 1973). When we tested these predictions experimentally, the C-type payoffs were the highest in CT. In this environment the average observed C-type payoff was even higher than the maximum equilibrium payoff. In CT about half of the D-types did not mimic the communication behavior of C-types, and hence even cheap talk revealed some information to the C-types. This indicates that half of the D-types were reluctant to make promises they would break. We introduce a theoretical model with promise-keepers. When the probability of an agent being promise-keeper is around 50%, the signaling rate will be higher in CT than in FC. On the other hand, for the same signal structure C-types choose more often H in the FC than in CT. These predictions are confirmed by the experimental results. Overall, the effect of the higher signalling rate in CT dominates: Together with presence of promise-keepers the higher signalling rate allows the C-types to coordinate more often on the \good" (H;H) outcome in CT, resulting in higher C-type payoffs in CT than in FC. |
| Keywords: | Asymmetric information; coordination; credible communication |
| JEL: | C7 C9 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15843&r= |
| By: | Michael Finus (University of Graz, Austria); Francesco Furini (University of Hamburg, Germany and Università Ca’ Foscari Venezia, Italy); Anna Viktoria Rohrer (University of Graz, Austria) |
| Abstract: | We analyze the paradox of cooperation, as established by Barrett (1994), and later reiterated by many others, in a more general framework. That is, we show that stable coalitions are either small or if they are large, the potential gains from cooperation are small. First, we argue that the extension to a mitigation-adaptation game is a generalization of Barrett’s pure mitigation game. Second, we consider for this extension not only the Nash-Cournot scenario, as in Bayramoglu et al. (2018), but also the Stackelberg scenario. Third, we show generally that if mitigation levels in different countries are strategic substitutes, stable coalitions are larger in the Stackelberg than in the Nash-Cournot scenario. Fourth, this is reversed if mitigation levels are strategic complements, which is possible if the strategic interaction between mitigation and adaptation is sufficiently strong. Fifth, for all possible combination of assumptions, we demonstrate that the paradox of cooperation is robust, except if mitigation and adaptation were strategic complements, which we argue is an assumption not supported by empirical evidence. |
| Keywords: | Climate change; mitigation-adaptation game; international environmental agreements; paradox of cooperation; Nash-Cournot versus Stackelberg scenario. |
| JEL: | C72 F12 F18 H23 Q58 |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:grz:wpaper:2021-04&r= |
| By: | Castaneda Dower, Paul; Gokmen, Gunes; Le Breton, Michel; Weber, Shlomo |
| Abstract: | This paper examines the lasting impact of the alignment of African countries during the Cold War on modern economic development. We show that the division of the continent into two blocs (East/West) led to two clusters of development outcomes that reflect the Cold War's ideological divide. To determine alignment, we introduce a non-cooperative game of social interactions between African countries, where every country chooses one of two existing blocs based on its predetermined bilateral similarities with other members of the bloc. We show the existence of a strong Nash equilibrium in our game and apply the celebrated MaxCut method to identify such a partition. We validate the alignment by confirming that it predicts UN General Assembly voting patterns during the Cold War. Our approach, linking global political interdependence to distinct development paths in Africa, extracts from history a micro-founded, exogenous treatment, while allowing for an endogenous, process-oriented view of historical events. |
| Keywords: | Africa; blocs; Cold War; Development Clusters; Landscape theory; Political Alliances; Strong Nash Equilibrium |
| JEL: | C62 C72 F54 F55 N47 O19 O57 Y10 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15810&r= |
| By: | Asker, John; Baccara, Mariagiovanna; Lee, SangMok |
| Abstract: | Auctioneers of patents are observed to allow joint bidding by coalitions of buyers. These auctions are distinguished from standard ones by the patents being non-rivalrous, but still excludable, in consumption--that is, they are club goods. This affects the way coalitional bidding impacts auction performance. We study the implications of coalitions of bidders on second-price (or equivalently, ascending-price) auctions. Although the formation of coalitions per se can benefit the seller, we show that stable coalition profiles tend to consist of excessively large coalitions, to the detriment of both auction revenue and social welfare. We show that limiting the permitted coalition size increases efficiency and confers benefits on the seller. Lastly, we compare the revenues generated by patent auctions and multi-license auctions, and we find that the latter are superior in a large class of environments. |
| Keywords: | asymmetric auctions; Club goods; Intellectual Property; patents |
| JEL: | D44 D47 K1 L14 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15703&r= |
| By: | Ahrash Dianat; Mikhail Freer |
| Abstract: | We provide the first direct test of how the credibility of an auction format affects bidding behavior and final outcomes. To do so, we conduct a series of laboratory experiments where the role of the seller is played by a human subject who receives the revenue from the auction and who (depending on the treatment) has agency to determine the outcome of the auction. We find that a large majority of bids in the non-credible version of the second-price auction lie between the theoretical benchmarks of the first-price auction and the credible second-price auction. While sellers in the non-credible second-price auction often break the rules of the auction and overcharge the winning bidder, they typically do not maximize revenue. We provide a behavioral explanation for our results based on incorrect beliefs (on the part of bidders) and aversion to rule-breaking (on the part of sellers), which is confirmed by revealed preference tests. |
| Date: | 2021–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2105.00204&r= |
| By: | Imre Fertõ (Institute of Economics, Centre for Economic and Regional Studies,Budapest, Hungary and Kaposvár University, Kaposvár, Hungary); László Á. Kóczy (Institute of Economics, Centre for Economic and Regional Studies,Budapest, Hungaryand Department of Finance, Budapest University of Technology and Economics, Hungary); Kovács Attila (Károli Gáspár University of the Reformed Church, Budapest, HungaryBudapest, Hungary); Balázs R. Sziklai (Institute of Economics, Centre for Economic and Regional Studies,Budapest, Hungary and Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, Hungary) |
| Abstract: | We aim to identify the most influential members of the Agricultural Committee of the European Parliament (COMAGRI). Unlike previous studies that were based on case studies or interviews with stakeholders, we analyse the voting power of MEPs using a spatial Banzhaf power index. We identify critical members: members whose votes are necessary to form winning coalitions. We found that rapporteurs, EP group coordinators and MEPs from countries with high relative Committee representations, such as Ireland, Poland or Romania are powerful actors. Italy emerges as the most influential member state, while France seems surprisingly weak. |
| Keywords: | European Parliament, Common Agricultural Policy, voting games, Banzhaf index, voting game over a convex geometry |
| JEL: | D71 D72 Q18 |
| Date: | 2021–03 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:2114&r= |
| By: | Mehmet Ekmekci; Hanzhe Zhang |
| Abstract: | We study two-sided reputational bargaining with opportunities to issue an ultimatum -- threats to force dispute resolution. Each player is either a justified type, who never concedes and issues an ultimatum whenever an opportunity arrives, or an unjustified type, who can concede, wait, or bluff with an ultimatum. In equilibrium, the presence of ultimatum opportunities can harm or benefit a player by decelerating or accelerating reputation building. When only one player can issue an ultimatum, equilibrium play is unique. The hazard rate of dispute resolution is discontinuous and piecewise monotonic in time. As the probabilities of being justified vanish, agreement is immediate and efficient, and if the set of justifiable demands is rich, payoffs modify Abreu and Gul (2000), with the discount rate replaced by the ultimatum opportunity arrival rate if the former is smaller. When both players' ultimatum opportunities arrive sufficiently fast, there may exist multiple equilibria in which their reputations do not build up and negotiation lasts forever. |
| Date: | 2021–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2105.01581&r= |
| By: | Shweta Gaonkar; Angelo Mele |
| Abstract: | How do inter-organizational networks emerge? Accounting for interdependence among ties while studying tie formation is one of the key challenges in this area of research. We address this challenge using an equilibrium framework where firms' decisions to form links with other firms are modeled as a strategic game. In this game, firms weigh the costs and benefits of establishing a relationship with other firms and form ties if their net payoffs are positive. We characterize the equilibrium networks as exponential random graphs (ERGM), and we estimate the firms' payoffs using a Bayesian approach. To demonstrate the usefulness of our approach, we apply the framework to a co-investment network of venture capital firms in the medical device industry. The equilibrium framework allows researchers to draw economic interpretation from parameter estimates of the ERGM Model. We learn that firms rely on their joint partners (transitivity) and prefer to form ties with firms similar to themselves (homophily). These results hold after controlling for the interdependence among ties. Another, critical advantage of a structural approach is that it allows us to simulate the effects of economic shocks or policy counterfactuals. We test two such policy shocks, namely, firm entry and regulatory change. We show how new firms' entry or a regulatory shock of minimum capital requirements increase the co-investment network's density and clustering. |
| Date: | 2021–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2105.00458&r= |
| By: | Canidio, Andrea; Karle, Heiko |
| Abstract: | Two players with preferences distorted by the focusing effect (Koszegi and Szeidl, 2013) negotiate an agreement over several issues and one transfer. Our main result is that, as long as their preferences are differentially distorted, an issue will be inefficiently left out of the agreement or inefficiently included in the agreement whenever the importance of the other issues on the table is sufficiently large. When this is the case, the salience of the transfer dimension is large for both players, but differentially so, therefore creating a form of disagreement between them. In extreme cases, this could lead to an inefficient breakdown of the negotiation. Anticipating this possibility, the negotiating parties may negotiate in stages, by first signing an incomplete agreement and later finalizing the outcome of the negotiation. As in Raiffa (1982), these incomplete agreements may impose bounds on some dimensions of the bargaining solution in order to reduce their salience. |
| Keywords: | Bargaining; Focusing Effect; Incomplete Agreements; negotiations; Salience |
| JEL: | C78 D03 D86 F51 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15698&r= |
| By: | Ana Babus; Cecilia Parlatore |
| Abstract: | We study the determinants of asset market fragmentation in a model with strategic investors that disagree about the value of an asset. Investors' choices determine the market structure. Fragmented markets are supported in equilibrium when disagreement between investors is low. In this case, investors take the same side of the market and are willing to trade in smaller markets with a higher price impact to face less competition when trading against a dealer. The maximum degree of market fragmentation increases as investors' priors are more correlated. Dealers can benefit from fragmentation, but investors are always better off in centralized markets. |
| JEL: | D43 D47 G12 |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:28729&r= |
| By: | Alonso, Ricardo; Zachariadis, Konstantinos |
| Abstract: | A regulator who designs a public stress test to elicit private investment in a distressed bank must account for large investors' private information on the bank's state. We provide conditions for crowding-in (crowding-out) so that the regulator offers more (less) information to better-informed investors. Crowding-in obtains if investors' private information is not too discriminating of the state. We show that the region of the common prior is consequential: if crowding-in occurs for ex-ante optimistic investors then crowding-out follows if they were instead pessimistic. Investors' value from more precise private signals may come from the effect on the public test's precision. |
| Keywords: | Bayesian persuasion; Endogenous Public Signal; Financial disclosure; information design; stress tests |
| JEL: | D83 G21 G28 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15792&r= |
| By: | Cieslak, Anna; Malamud, Semyon; Schrimpf, Andreas |
| Abstract: | We study the general problem of Bayesian persuasion (optimal information design) with continuous actions and continuous state space in arbitrary dimensions. First, we show that with a finite signal space, the optimal information design is always given by a partition. Second, we take the limit of an infinite signal space and characterize the solution in terms of a Monge-Kantorovich optimal transport problem with an endogenous information transport cost. We use our novel approach to: 1. Derive necessary and sufficient conditions for optimality based on Bregman divergences for non-convex functions. 2. Compute exact bounds for the Hausdorff dimension of the support of an optimal policy. 3. Derive a non-linear, second-order partial differential equation whose solutions correspond to regular optimal policies. We illustrate the power of our approach by providing explicit solutions to several non-linear, multidimensional Bayesian persuasion problems. |
| Keywords: | Bayesian persuasion; information design; signalling |
| JEL: | D82 D83 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15859&r= |
| By: | Paolo Bertoletti |
| Abstract: | We propose a novel approach to study competition among platforms. In particular, we consider representative consumer’s preferences over the services platforms provide and the commodities they intermediate. Platforms are assumed to be large, intermediating a variety of commodities offered by sellers under monopolistic competition and free entry, and competing à la Cournot. We use a duopoly setting to discuss the welfare implications of platform exchange commissions, which are typically significant in real-world cases. Our preliminary finding is that positive commission actually worsens consumer welfare by reducing the platform price-adjusted quality indexes. |
| Keywords: | platform competition, two-sided markets, market intermediation |
| JEL: | D11 L13 L41 L51 |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:mib:wpaper:468&r= |
| By: | Vincent Martinet (INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Pedro Gajardo; Michel de Lara |
| Abstract: | Applying the solutions defined in the axiomatic bargaining theory to actual bargaining problems is a challenge when the problem is not described by its Utility Possibility Set (UPS) but as an economic environment specifying the set of alternatives and utility profile underlying the UPS. We introduce the axioms of Independence of Non-Efficient Alternatives and Independence of Redundant Alternatives. A solution satisfying these axioms can be applied to a simplified problem based on any reduced set of alternatives generating the Pareto frontier of the initial problem, and produces the same outcome. We compare our axioms to usual independence axioms, and show that they are satisfied by many usual bargaining solutions. Then, we introduce monotonicity conditions corresponding to the existence of an interest group (i.e., agents ranking the alternatives in the same order). For such monotonic economic environments, we provide a parameterized family of alternatives that generates the Pareto frontier of the bargaining problem, in line with our previous results. Our analysis illustrates that an axiomatic approach can be useful to foster the application of bargaining solutions, in complement to usual computational methods. |
| Date: | 2021–04–23 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03206724&r= |
| By: | Li, Xiaolin; Özer, Özalp; Subramanian, Upender |
| Abstract: | Cheap-talk communication between parties with conflicting interests is common in many business and economic settings. Two distinct behavioral economics theories, the trust-embedded model and the level-k model, have emerged to explain how cheap talk works between human decision makers. The trust-embedded model considers that decision makers are motivated by nonpecuniary motives to be trusting and trustworthy. In contrast, the level-k model considers that decision makers are purely self-interested but limited in their ability to think strategically. Although both theories have been successful in explaining cheap-talk behaviors in separate contexts, they point to contrasting drivers for human behaviors. In this paper, we provide the first direct comparison of both theories within the same context. We show that, in a cheap-talk setting that well represents many practical situations, the two models make characteristically distinct and empirically distinguishable predictions. We leverage past experiment data from this setting to determine what aspects of cheap-talk behavior each model captures well and which model (or combination of models) has better explanatory power and predictive performance. We find that the trust-embedded model emerges as the dominant explanation. Our results, thus, highlight the importance of investing in systems and processes to foster trusting and trustworthy relationships in order to facilitate more effective cheap-talk interactions. |
| Keywords: | behavioral economics; bounded rationality; cheap talk; level-k thinking; trust; trustworthiness |
| JEL: | J50 |
| Date: | 2021–03–22 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:107103&r= |
| By: | Alain Jean-Marie (NEO - Network Engineering and Operations - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique); Tania Jimenez (LIA - Laboratoire Informatique d'Avignon - AU - Avignon Université - Centre d'Enseignement et de Recherche en Informatique - CERI); Tidball Mabel (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UMR 5211 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | We introduce the family of Conjectural Learning procedures, in which agents form conjectures about what the opponent will play, as a function of their action or some state variable. We prove general properties of these procedures, comparing them to two dynamic systems generated by nearsighted agents solving repeatedly a static game, either cooperatively, or noncooperatively. We then specify three simple functional forms of conjectures and analyze the five resulting dynamic systems, in terms of steady states and convergence conditions. We next further specify these procedures to the case of a game of groundwater management, using a quadratic functional form for the profit function of agents. We obtain then explicit expressions for steady states and convergence conditions for the dynamic systems. Finally, we conduct numerical experiments in order to assess the "performance" of pairs of agents adopting each of the five behaviors. |
| Abstract: | Nous définissons une famille de procédures d'apprentissage conjectural, dans laquelle les agents formulent des conjectures au sujet de ce que l'adversaire va jouer, en fonction de leur propre action ou d'une variable d'état. Nous prouvons des propriétés générales de ces procédures, en les comparant aux deux systèmes dynamiques générés par des agents myopes qui résolvent à chaque étape un jeu statique, soit de façon coopérative, soit noncoopérative. Nous spécifions ensuite trois formes fonctionnelles simples pour les conjectures et nous analysons les cinq systèmes dynamiques ainsi définis, en termes d'états stationnaires et de conditions de convergence. Puis nous appliquons ces procédures pour un problème de gestion d'une nappe phréatique, en utilisant une forme fonctionnelle quadratique pour la fonction de profit des agents. Nous obtenons alors des formules explicites pour les états stationnaires et des conditions de convergence pour les systèmes dynamiques. Finalement, nous menons des expériences numériques afin d'évaluer les "performances" de paires d'agents qui adoptent chacun des cinq comportements. |
| Keywords: | Dynamic,Learning,Natural Resources Management,Game Theory,Théorie des Jeux,Dynamique,Apprentissage,Gestion de Ressources Naturelles |
| Date: | 2021–04–30 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03213518&r= |