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on Game Theory |
| By: | Pierpaolo Battigalli; Roberto Corrao; Martin Dufwenberg |
| Abstract: | Psychological game theory (PGT), introduced by Geanakoplos, Pearce & Stacchetti (1989) and signi cantly generalized by Battigalli & Dufwenberg (2009), extends the standard game theoretic framework by letting playersutility at endnodes depend on their interactive beliefs. While it is understood that a host of applications that model and/or test the role of emotional and other psychological forces nd their home in PGT, the framework is abstract and comprises complex mathematical objects, such as playersin nite hierarchies of beliefs. Thus, PGT provides little guidance on how to model speci c belief-dependent motivations and use them in game theoretic analysis. This paper takes steps to fi ll this gap. Some aspects are simplifi ed e.g., which beliefs matter but others are refi ned and brought closer to applications by providing more structure. We start with belief-dependent motivations and show how to embed them in game forms to obtain psychological games. We emphasize the role of time and of the perception of players' intentions. We take advantage of progress made on the foundations of game theory to expand and improve on PGT solution concepts. JEL classi fication: C72; C73; D81; D82; D92Keywords: Psychological game theory; Belief-dependent motivation; Intentions; Time; Rationalizability; Self-confi rming equilibrium; Bayesian sequential equilibrium |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:642&r=all |
| By: | Abhijit Ramalingam; Antonio J. Morales; James M. Walker |
| Abstract: | This study brings together two strands of experimental literature, “Give and Take” versions of strategically and payoff isomorphic linear public goods games and the effectiveness of peer punishment in promoting cooperation in repeated fixed-group game settings. We find evidence of lower cooperation in the Take game setting, primarily due to a greater decrease in cooperation in later decision rounds. Importantly, we also find that peer punishment is able to overcome the decrease in cooperation in the Take game, leading to greater relative increases in cooperation and earnings. Overall, with punishment, we observe efficiency gains in the Take game, but not in the Give game. This result is linked to the fact that low contributors in their respective groups are targeted for punishment more frequently in the Take game than in the Give game. Key Words: isomorphic, social dilemma, experiment, cooperation, punishment, reciprocal preferences |
| JEL: | C72 C91 C92 D02 H41 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:apl:wpaper:18-15&r=all |
| By: | Tanaka, Yasuhito |
| Abstract: | This paper studies a Stackelberg type symmetric dynamic $n$-players zero-sum game. There is one leader and $n-1$ followers. Players have the symmetric payoff functions. The game is a two-stages game. In the first stage the leader determines the value of its strategic variable. In the second stage the followers determine the values of their strategic variables given the value of the leader's strategic variable. In the static game, on the other hand, all players simultaneously determine the values of their strategic variable. We do not assume differentiability of payoff functions. This paper shows that the sub-game perfect equilibrium of the Stackelberg type symmetric dynamic zero-sum game is equivalent to the equilibrium of the static game if and only if the game is fully symmetric. |
| Keywords: | Stackelberg equilibrium, leader, follower, dynamic symmetric zero-sum game |
| JEL: | C72 |
| Date: | 2019–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:91898&r=all |
| By: | Tanaka, Yasuhito |
| Abstract: | We consider a Stackelberg type symmetric dynamic three-players zero-sum game. One player is the leader and two players are followers. All players have the symmetric payoff functions. The game is a two-stages game. In the first stage the leader determines the value of its strategic variable. In the second stage the followers determine the values of their strategic variables given the value of the leader's strategic variable. On the other hand, in the static game all players simultaneously determine the values of their strategic variable. We do not assume differentiability of players' payoff functions. We show that the sub-game perfect equilibrium of the Stackelberg type symmetric dynamic zero-sum game with a leader and two followers is equivalent to the equilibrium of the static game if and only if the game is fully symmetric. |
| Keywords: | symmetric zero-sum game, Stackelberg equilibrium, leader, follower |
| JEL: | C72 |
| Date: | 2019–02–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:91919&r=all |
| By: | Giovanni Compiani (Institute for Fiscal Studies); Phil Haile (Institute for Fiscal Studies and Yale University); Marcelo Sant'Anna (Institute for Fiscal Studies) |
| Abstract: | An oil lease auction is the classic example motivating a common values model. However, formal testing for common values has been hindered by unobserved auction-level heterogeneity, which is likely to affect both participation in an auction and bidders' willingness to pay. We develop and apply an empirical approach for fi rst-price sealed bid auctions with affiliated values, unobserved heterogeneity, and endogenous bidder entry. The approach also accommodates spatial dependence and sample selection. Following Haile, Hong and Shum (2003), we specify a reduced form for bidder entry outcomes and rely on an instrument for entry. However, we relax their control function requirements and demonstrate that our specifi cation is generated by a fully speci fied game motivated by our application. We show that important features of the model are nonparametrically identifi ed and propose a semiparametric estimation approach designed to scale well to the moderate sample sizes typically encountered in practice. Our empirical results show that common values, affiliated private information, and unobserved heterogeneity - three distinct phenomena with different implications for policy and empirical work - are all present and important in U.S. offshore oil and gas lease auctions. We find that ignoring unobserved heterogeneity in the empirical model obscures the presence of common values. We also examine the interaction between affiliation, the winner's curse, and the number of bidders in determining the aggressiveness of bidding and seller revenue. |
| Date: | 2018–07–03 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:37/18&r=all |
| By: | Shaun P. Hargreaves Heap; Abhijit Ramalingam; Brock K. Stoddard |
| Abstract: | In experiments, contributions to a team public good increase when the team is placed in a competition with another team for prize. This paper is concerned with whether this insight generalises to teams that are internally unequal. In the experiment we report, it does. Indeed, the boost to public goods contributions is bigger with unequal teams than equal ones. We also find that the boost to contributions is most significant among the ‘rich’ in the team. Hence, since the public good is shared equally, competition not only promotes efficiency, it also reduces inequality in our experiment. Key Words: public goods, experiment, team competition, inequality, within group, productivity |
| JEL: | C72 C91 C92 D31 D63 D72 H41 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:apl:wpaper:18-17&r=all |
| By: | Abhijit Ramalingam; Brock K. Stoddard; James M. Walker |
| Abstract: | In a laboratory setting, we investigate the effect of competition for the resources of team members with ‘divided loyalties’, and the role of such competition in overcoming the free-rider problem associated with the provision of team-level public goods. We find that competition alone creates ‘winners’ and ‘losers’. However, if groups have access to more information on the actions of team members, or are able to determine their membership through ostracism, they are more successful in attracting the ‘loyalties’ of team members. By eschewing the study of additional mechanisms that require external intervention or alterations of payoff functions, our work highlights the potential of implicit competition in promoting cooperation. Key Words: public goods, experiment, divided loyalties, competition, resources, endogenous membership |
| JEL: | C72 C91 C92 H41 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:apl:wpaper:18-18&r=all |
| By: | Kamei, Kenju |
| Abstract: | Exogenously imposed infinite repetition is known to mitigate people’s uncooperative behaviors in dilemma situations with partner matching through personal enforcement. One as yet unanswered question is whether people collectively choose to interact with each other under the partner matching condition when there exists an alternative possibility under random matching. In an indefinitely repeated public goods game framework, I let subjects democratically choose whether to (i) play with pre-assigned specific others for all rounds or to (ii) play with randomly matched counterparts in every round. The experimental results revealed that most groups collectively opt for the partner matching protocol. The data also indicated that groups achieve a higher level of cooperation when they democratically select the partner matching protocol by voting, relative to when the same option is exogenously imposed. These findings imply that people’s equilibrium selection may be affected by how the basic rules of games are introduced (endogenously or exogenously). The paper provides further evidence to suggest that the positive effect of democratic decision-making is stronger when the majority voting rule, rather than the unanimity rule, is applied. |
| Keywords: | experiment, public goods, cooperation, dilemma, social norms, endogenous choices |
| JEL: | C72 C73 C92 H41 |
| Date: | 2019–02–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:92097&r=all |
| By: | Hassan Najafi Alishah; Pedro Duarte; Telmo Peixe |
| Abstract: | For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model wchich encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes and edges. This piecewise linear flow is easy to compute even in higher dimensions, which allows the usage of numeric algorithms to find invariant dynamical structures such as periodic, homoclinic or heteroclinic orbits, which if robust persist as invariant dynamical structures of the original flow. We apply this method to prove the existence of chaotic behavior in some Hamiltonian replicator systems on the five dimensional simplex. |
| Keywords: | Flows on polytopes, Asymptotic dynamics, Heteroclinic networks, Poincaré maps, Hyperbolicity, Chaos, Evolutionary game theory |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:ise:remwps:wp0702019&r=all |
| By: | Fabien Prieur; Ingmar Schumacher; Martin Quaas |
| Abstract: | The option to tackle climate change by means of Solar Radiation Management (SRM) is mostly thought to reduce efforts of mitigating greenhouse gas emissions. Here we hypothesize that (i) a unilateral threat to employ SRM can induce players to commit to strategies with increased mitigation effort compared to what would be observed at the Nash equilibrium in emission strategies only and (ii) there exists a way to share the burden imposed by commitment to avoid SRM that Pareto dominates an alternative that would involve too high current emission levels then followed by future SRM deployment. To study these hypotheses we develop a two-region, two-stage, two-period game where regions choose mitigation and SRM. While SRM targets regional climate preferences, in line with current scientific evidence its deployment leads to uncertain damages on the other region. We first develop the general theory and then study a more specific linear-quadratic application. Finally we calibrate the model to real-world data and find that hypothesis (ii) holds for plausible values. |
| Keywords: | climate change, solar radiation management, heterogeneous damages, strategic interaction, commitment |
| JEL: | C72 Q54 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:drm:wpaper:2019-3&r=all |
| By: | Teresa Estañ (Centro de Investigación Operativa (CIO), Universidad Miguel Hernández de Elche.); Natividad Llorca (Centro de Investigación Operativa (CIO), Universidad Miguel Hernández de Elche.); Ricardo Martínez (Department of Economic Theory and Economic History, University of Granada.); Joaquín Sánchez-Soriano (Centro de Investigación Operativa (CIO), Universidad Miguel Hernández de Elche..) |
| Abstract: | In this study, we consider different cities located along a tram line. Each city may have one or several stations and information is available about the flow of passengers between any pair of stations. A fixed cost (salaries of the executive staff, repair facilities, or fixed taxes) must be divided among the cities. This cost is independent of the number of passengers and the length of the line. We propose a mathematical model to identify suitable mechanisms for sharing the fixed cost. In the proposed model, we propose, and characterize axiomatically, three rules, which include the uniform split, the proportional allocation and a intermediate situation. The analyzed axioms represent the basic requirements for fairness and elemental properties of stability. |
| Keywords: | axiom, cost game, cost sharing, fairness, transport networks. |
| Date: | 2019–02–05 |
| URL: | http://d.repec.org/n?u=RePEc:gra:wpaper:19/03&r=all |
| By: | Serafin J. Grundl; Yu Zhu |
| Abstract: | In laboratory experiments bidding in first-price auctions is more aggressive than predicted by the risk-neutral Bayesian Nash Equilibrium (RNBNE) - a finding known as the overbidding puzzle. Several models have been proposed to explain the overbidding puzzle, but no canonical alternative to RNBNE has emerged, and RNBNE remains the basis of the structural auction literature. Instead of estimating a particular model of overbidding, we use the overbidding restriction itself for identification, which allows us to bound the valuation distribution, the seller's payoff function, and the optimal reserve price. These bounds are consistent with RNBNE and all models of overbidding and remain valid if different bidders employ different bidding strategies. We propose simple estimators and evaluate the validity of the bounds numerically and in experimental data. |
| Keywords: | Experimental findings ; First-price auction ; Partial identification ; Robust inference ; Structural estimation |
| JEL: | C14 D44 |
| Date: | 2019–02–07 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2019-06&r=all |
| By: | Cécile Bazart (CEEM, University of Montpellier, Avenue Raymond Dugrand - site Richter C.S. 79606, 34960 Montpellier, France); Mathieu Lefebvre (BETA, University of Strasbourg, 61 avenue de la Forêt Noire, 67085 Strasbourg, France); Julie Rosaz (Univ Lyon, Université Lumière Lyon 2, GATE UMR 5824, F-69130 Ecully, France) |
| Abstract: | In a series of experiments, we test the relative efficiency of persuasion and commitment schemes to increase and sustain contribution levels in a Voluntary Contribution Game. The design allows to compare a baseline consisting of a repeated public good game to, respectively, four manipulation treatments relying on: an information strategy, a low commitment strategy, a high commitment strategy and a promise strategy. We confirm the advantages of psychologically orientated policies as they increase the overall level of contribution and for some, that is commitment and promises, question the decreasing trend traditionally observed in long term contributions to public goods. |
| Keywords: | Experiment, Persuasion, Commitment, Voluntary Contribution Mechanism |
| JEL: | C91 D91 H41 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:1907&r=all |
| By: | Telmo Peixe |
| Abstract: | Generally a biological system is said to be permanent if under small perturbations none of the species goes to extinction. In 1979 P. Schuster, K. Sigmund, and R. Wolff [14] introduced the concept of permanence as a stability notion for systems that models the self-organization of biological macromolecules. After, in 1987 W. Jansen [8], and J. Hofbauer and K. Sigmund [5] give sufficient conditions for permanence in the usual replicators. In this paper we extend these results for polymatrix replicators. |
| Keywords: | Permanence,Polymatrix Replicator,Stability,Replicator equation,Evolutionary game theory,Lotka-Volterra. |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:ise:remwps:wp0692019&r=all |
| By: | Didier Laussel (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Two duopolists first decide in which proportions to incorporate in their product two different Lancasterian characteristics and then compete in quantities or prices. In the Cournot case, minimum differentiation obtains at equilibrium whatever the degree of substituability between the characteristics. In the Bertrand one, the equilibrium depends crucially on the degree of substituability/complementarity between the two characteristics. Maximal differential obtains if and only if the characteristics are strong enough substitutes. On the contrary as characteristics become closer and closer complements one obtains in the limit a minimal differentiation result. JEL Codes: L13. Keyword: Horizontal Product Differentiation, Lancasterian Characteristics. |
| Keywords: | Horizontal Product Differentiation,Lancasterian Characteristics.,Duopoly |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-01992047&r=all |
| By: | William Brock; Anastasios Xepapadeas |
| Abstract: | We study climate change policies by using the novel pattern scaling approach of regional transient climate response to develop an economyclimate model under conditions of deep uncertainty associated with: (i) temperature dynamics, (ii) regional climate change damages, and (iii) policy in the form of carbon taxes. We analyze both cooperative and noncooperative outcomes in a regional model. Under deep uncertainty, robust control policies are more conservative regarding emissions, the higher the aversion to ambiguity, while damage uncertainty seems to produce more conservative behavior than climate dynamics uncertainty. Cooperative policies tend to be more conservative than noncooperative policies for similar concerns about uncertainty but, as concerns about uncertainty increase, policies tend to move closer to each other. Asymmetries in concerns about uncertainty tend to produce large deviations in regional emissions policy at the noncooperative solution. If aversion to ambiguity is sufficiently high, optimal regulation aiming to attain a cooperative steady state or a steady state that satisfies conditions for a Nash equilibrium might not be possible. The result is associated with the existence of regional hot spots and temperature spillovers across regions, a situation which emerges in the real world. In such cases, deep uncertainty about the impacts of climate change makes robust regulation infeasible. |
| Keywords: | Regional climate change policy, Regional temperature anomalies, Deep uncertainty, Robust control, Cooperative and noncooperative solutions. |
| JEL: | Q54 Q58 D81 |
| Date: | 2019–01–26 |
| URL: | http://d.repec.org/n?u=RePEc:aue:wpaper:1901&r=all |
| By: | Charles-Albert Lehalle (Chevreux Research Department - Chevreux SA); Charafeddine Mouzouni (ICJ - Institut Camille Jordan [Villeurbanne] - CNRS - Centre National de la Recherche Scientifique - UJM - Université Jean Monnet [Saint-Étienne] - ECL - École Centrale de Lyon - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon) |
| Abstract: | This paper goes beyond the optimal trading Mean Field Game model introduced by Pierre Cardaliaguet and Charles-Albert Lehalle in [Cardaliaguet, P. and Lehalle, C.-A., Mean field game of controls and an application to trade crowding, Mathematics and Financial Economics (2018)]. It starts by extending it to portfolios of correlated instruments. This leads to several original contributions: first that hedging strategies naturally stem from optimal liquidation schemes on portfolios. Second we show the influence of trading flows on naive estimates of intraday volatility and correlations. Focussing on this important relation, we exhibit a closed form formula expressing standard estimates of correlations as a function of the underlying correlations and the initial imbalance of large orders, via the optimal flows of our mean field game between traders. To support our theoretical findings, we use a real dataset of 176 US stocks from January to December 2014 sampled every 5 minutes to analyze the influence of the daily flows on the observed correlations. Finally, we propose a toy model based approach to calibrate our MFG model on data. |
| Date: | 2019–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02003143&r=all |