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on Game Theory |
| By: | Grabisch, Michel (Paris School of Economics); Sudhölter, Peter (Department of Business and Economics) |
| Abstract: | A balanced transferable utility game (N, v) has a stable core if its core is externally stable, that is, if each imputation that is not in the core is dominated by some core element. Given two payoff allocations x and y, we say that x outvotes y via some coalition S of a feasible set if x dominates y via S and x allocates at least v(T ) to any feasible T that is not contained in S. It turns out that outvoting is transitive and the set M of maximal elements with respect to outvoting coincides with the core if and only if the game has a stable core. By applying the duality theorem of linear programming twice, it is shown that M coincides with the core if and only if a certain nested balancedness condition holds. Thus, it can be checked in finitely many steps whether a balanced game has a stable core. We say that the game has a super-stable core if each payoff vector that allocates less than v(S) to some coalition S is dominated by some core element and prove that core super-stability is equivalent to vital extendability, requiring that each vital coalition is extendable. |
| Keywords: | Domination; stable set; core; TU game |
| JEL: | C71 |
| Date: | 2020–06–15 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2020_006&r=all |
| By: | Ekmekci, Mehmet; Maestri, Lucas |
| Abstract: | We introduce a class of two-player dynamic games to study the effectiveness of screening in a principal-agent problem. In every period, the principal chooses either to irreversibly stop the game or to continue, and the agent chooses an action if the principal chooses to continue. The agent’s type is his private information, and his actions are imperfectly observed. Players’ flow payoffs depend on the agent’s action, and players’ lump-sum payoffs when the game stops depends on the agent’s type. Both players are long-lived and share a common discount factor. We study the limit of the equilibrium outcomes as both players get arbitrarily patient. Nash equilibrium payoff vectors converge to the unique Nash equilibrium payoff vector of an auxiliary, two-stage game with observed mixed actions. The principal learns some but not all information about the agent’s type. Any payoff-relevant information revelation takes place at the beginning of the game. We calculate the probability that the principal eventually stops the game, against each type of the agent. |
| Keywords: | Dynamic Games, Screening, Reputation, Imperfect Monitoring |
| JEL: | C73 D82 D86 |
| Date: | 2019–08–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:100885&r=all |
| By: | V. K. Oikonomou; J. Jost |
| Abstract: | At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff does not depend on the opponent's action. Here, we generalize this to multi-player simultaneous perfect information strategic form games. We show that also in this class of games, there always exists at least one periodic strategy, and we investigate the mathematical properties of such periodic strategies. In addition, we demonstrate that periodic strategies may exist in games with incomplete information; we shall focus on Bayesian games. Moreover we discuss the differences between the periodic strategies formalism and cooperative game theory. In fact, the periodic strategies are obtained in a purely non-cooperative way, and periodic strategies are as cooperative as the Nash equilibria are. Finally, we incorporate the periodic strategies in an epistemic game theory framework, and discuss several features of this approach. |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2005.12832&r=all |
| By: | José Pedro Pontes |
| Abstract: | In this paper, we use HARSANYI and SELTEN (1988)’s risk dominance concept to explain the growth in the Portuguese higher education system during two time periods: 1998 2005 and 2005-2018. During the first time period, the high annual growth rate in tertiary schooling (8.2%) can be accounted for by a n – person, k – coordination Stag Hunt game framework. Hence, the progress in university education can be described as the outcome of a noncooperative game, where youngsters and their families can take decisions without needing to communicate previously. By contrast, during 2005-2018, the former coordination game seems inadequate to rationalize the continued progress in college schooling at an annual rate of 5%, since the wage premium of tertiary education fell drastically (more than 20%) during the same interval. Hence, we switch to an “unanimity” game as framework of analysis. Within such a game, the widespread tertiary enrolment can be accounted for a diminishing “unanimity” requirement, derived from a shrinking demography and the sheer cumulative effect of past spread of college education. We apply here NASH (1950, 1953)’s intuition that the selection of an equilibrium point within an unanimity game is a tool for modelling the outcome of a game, where the players discuss in order to reach an agreement. Hence, we can describe the rise in college education in Portugal in the more recent time period as the outcome of a cooperative process, leading to a wide policy consensus. |
| Keywords: | Education; Regional Development; Coordination Games; Risk Dominance |
| JEL: | C72 I20 O12 R11 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:ise:remwps:wp01332020&r=all |
| By: | Giorgio Fabbri (Univ.Grenoble Alpes, CNRS, INRIA, Grenoble INP, GAEL, Grenoble, France); Silvia Faggian (Department of Economics, University Of Venice Ca’ Foscari, Italy); Giuseppe Freni (Department of Business and Economics, University of Naples “Parthenope”, Naples, Italy.) |
| Abstract: | We study the dynamics of the exploitation of a natural resource, distributed in space and mobile, where spatial diversification is introduced by a network structure. Players are assigned to different nodes by a regulator, after he/she decides at which nodes natural reserves are established. The game solution shows how the dynamics of spatial distribution depends on the productivity of the various sites, on the structure of the connections between the various locations, and on the preferences of the agents. At the same time, the best locations to host a nature reserve are identified in terms of the parameters of the model, and it turns out they correspond to the most central (in the sense of eigenvector centrality) nodes of a suitably redefined network which takes into account the nodes productivities. |
| Keywords: | Harvesting, spatial models, differential games, nature reserve |
| JEL: | Q20 Q28 R11 C73 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2020:07&r=all |
| By: | Ai Takeuchi (College of Economics, Ritsumeikan University); Erika Seki (Graduate School of Economics, Osaka University) |
| Abstract: | This study considers the twin problems of free riding and coordination failure prevailing in the provision of multiple public goods with diminishing marginal returns in which the payoff-sum maximising Pareto optimal outcome requires less-than-full contributions by group members. We examine theoretically and experimentally whether the provision of information on the demand for public goods helps overcome these problems and improves efficiency. We construct a game of two public goods,each with an upper bound on effective contributions. Theoretical analysis predicts that this information improves efficiency as it prompts efficiency concerned individuals to match the upper bound of each public good in equilibrium.The experimental results show countervailing effects of demand information,i.e.,it improves coordination but deteriorates the free-riding problem. |
| Keywords: | Charity,Freeriding,Coordination,Multiplepublicgoods,Laboratoryexperiment, Information. |
| JEL: | C72 C91 C92 H41 |
| Date: | 2020–06 |
| URL: | http://d.repec.org/n?u=RePEc:osk:wpaper:1915r&r=all |
| By: | Hebert, Benjamin (Stanford U); La'O, Jennifer (Columbia U) |
| Abstract: | This paper analyzes non-fundamental volatility and efficiency in a class of large games (including e.g. linear-quadratic beauty contests) that feature strategic interaction and endogenous information acquisition. We adopt the rational inattention approach to information acquisition but generalize to a large class of information costs. Agents may learn not only about exogenous states, but also about endogenous outcomes. We study how the properties of the agents' information cost relate to the properties of equilibria in these games. We provide the necessary and sufficient conditions information costs must satisfy to guarantee zero non-fundamental volatility in equilibrium, and provide another set of necessary and sufficient conditions to guarantee equilibria are efficient. We show in particular that mutual information, the cost function typically used in the rational inattention literature, both precludes non-fundamental volatility and imposes efficiency, whereas the Fisher information cost introduced by Hebert and Woodford [2020] generates both non-fundamental volatility and inefficiency. |
| JEL: | C72 D62 D83 |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:3836&r=all |
| By: | Ren\'e A\"id; Luciano Campi; Liangchen Li; Mike Ludkovski |
| Abstract: | We study a new kind of non-zero-sum stochastic differential game with mixed impulse/switching controls, motivated by strategic competition in commodity markets. A representative upstream firm produces a commodity that is used by a representative downstream firm to produce a final consumption good. Both firms can influence the price of the commodity. By shutting down or increasing generation capacities, the upstream firm influences the price with impulses. By switching (or not) to a substitute, the downstream firm influences the drift of the commodity price process. We study the resulting impulse--regime switching game between the two firms, focusing on explicit threshold-type equilibria. Remarkably, this class of games naturally gives rise to multiple Nash equilibria, which we obtain via a verification based approach. We exhibit three types of equilibria depending on the ultimate number of switches by the downstream firm (zero, one or an infinite number of switches). We illustrate the diversification effect provided by vertical integration in the specific case of the crude oil market. Our analysis shows that the diversification gains strongly depend on the pass-through from the crude price to the gasoline price. |
| Date: | 2020–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2006.04382&r=all |
| By: | Mariola Ndrio; Subhonmesh Bose; Ye Guo; Lang Tong |
| Abstract: | Tie-line scheduling in multi-area power systems in the US largely proceeds through a market-based mechanism called Coordinated Transaction Scheduling (CTS). We analyze this market mechanism through a game-theoretic lens. Our analysis characterizes the effects of market liquidity, market participants' forecasts about inter-area price spreads, transaction fees and interaction of CTS markets with financial transmission rights. Using real data, we empirically verify that CTS bidders can employ simple learning algorithms to discover Nash equilibria that support the conclusions drawn from the equilibrium analysis. |
| Date: | 2020–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2006.03618&r=all |
| By: | Raouf Boucekkine (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, UCL IRES - Institut de recherches économiques et sociales - UCL - Université Catholique de Louvain); Giorgio Fabbri (GAEL - Laboratoire d'Economie Appliquée de Grenoble - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Salvatore Federico (DEPS - Dipartimento di Economia Politica e Statistica - UNISI - Università degli Studi di Siena); Fausto Gozzi (Dipartimento di Economia e Finanza [Roma] - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]) |
| Abstract: | In this paper, we revisit the theory of spatial externalities. In particular, we depart in several respects from the important literature studying the fundamental pollution free riding problem uncovered in the associated empirical works. First, instead of assuming ad hoc pollution diffusion schemes across space, we consider a realistic spatiotemporal law of motion for air and water pollution (diffusion and advection). Second, we tackle spatiotemporal non-cooperative (and cooperative) differential games. 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. We further provide with full exploration of the free riding problem, reflected in the so-called border effects. In particular, net pollution flows diffuse at an increasing rate as we approach the borders, with strong asymmetries under advection, and structural breaks show up at the borders. We also build a formal case in which a larger number of states goes with the exacerbation of pollution externalities. Finally, we explore how geographic discrepancies affect the shape of the border effects. |
| Keywords: | spatial externalities,environmental federalism,transboundary pollution,differential games in continuous time and space,infinite dimensional optimal control problems |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-02613177&r=all |
| By: | Jean-François Laslier (PSE - Paris School of Economics, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | I comment on the claim by John Roemer that \in games of pure coordination, Kantians drive Nashers to extinction". Using an explicit dynamic model of evolution, I notice that in these games, Kantian optimizers do not always drive sel sh optimizers to extinction. |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:psewpa:halshs-02652020&r=all |
| By: | Rabah Amir (University of Iowa - Henry B. Tippie College of Business - Department of Economics; Universidad de los Andes, Chile - School of Business and Economics); Igor V. Evstigneev (University of Manchester - Economics, School of Social Sciences); Thorsten Hens (University of Zurich - Department of Banking and Finance; Norwegian School of Economics and Business Administration (NHH); Swiss Finance Institute); Valeriya Potapova (University of Manchester); Klaus Reiner Schenk-Hoppé (University of Manchester - Department of Economics; Norwegian School of Economics (NHH) - Department of Finance) |
| Abstract: | The paper models evolution in pecunia in the realm of finance. Financial markets are explored as evolving biological systems. Investors pursuing diverse investment strategies compete for the market capital. Some `survive' and some `become extinct.' A central goal is to identify evolutionary stable, i.e. guaranteeing survival, investment strategies. The problem is studied in a framework combining stochastic dynamics and evolutionary game theory. The model proposed employs only objectively observable market data, in contrast with traditional settings relying upon unobservable investors characteristics (utilities and beliefs). The main result is a construction of an evolutionary stable strategy in the model at hand. |
| Keywords: | Evolutionary finance, financial markets, evolutionarily stable investment strategies, survival, stochastic dynamics, local stability |
| JEL: | C73 G11 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp2044&r=all |
| By: | Xu, Lili; Lee, Sang-Ho |
| Abstract: | This study considers a strategic interplay between corporate social responsibility (CSR) and privatization policy in a mixed market, and investigates the impact of the order of sequential games. We compare the different timeline of the game between the privatization-then-CSR and the reverse case of CSR-then-privatization, and highlight the significant role of the foreign shareholding ratio of the CSR-firm. We show that partial privatization is always optimal regardless of the timeline of the game, but the privatization-then-CSR yields a lower (higher) degree of privatization while a higher (lower) level of CSR than the CSR-then-privatization when the foreign penetration is sufficiently low (high). We also show that privatization-then-CSR can be a unique equilibrium in an endogenous timing game but socially desirable only when the foreign penetration is neither sufficiently low nor high. |
| Keywords: | Strategic CSR, Partial privatization, Foreign penetration, Mixed market |
| JEL: | L1 L2 M14 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:100770&r=all |
| By: | Gur, Yonatan (Stanford U); Macnamara, Gregory (Stanford U); Saban, Daniela (Stanford U) |
| Abstract: | In many marketplaces that facilitate trade with the objective of maximizing consumer surplus, prices are set by revenue-maximizing sellers but platforms can influence prices through (i) price-dependent promotion policies that can increase demand for a product by featuring it in a prominent position in the webpage and (ii) the information revealed to sellers about the value of being promoted. Identifying effective joint information design and promotion policies is a challenging dynamic problem as sellers can sequentially learn the promotion value from sales observations and update prices accordingly. We introduce the notion of confounding promotion policies, which are designed to prevent a Bayesian seller from learning the promotion value (at the expense of the short-run loss of diverting consumers from the best product offering). Leveraging these policies, we characterize the maximum long-run average consumer surplus that is achievable through joint information design and promotion policies when the seller sets prices myopically. We then establish a Bayesian Nash equilibrium by showing that the seller's best response to the platform's optimal policy is to price myopically at every history. The equilibrium we identify is platform-optimal within the class of horizon-maximin equilibria, in which strategies are not predicated on precise knowledge of the horizon length, and are designed to maximize payoff over the worst-case horizon. Our analysis allows one to identify effective platform policies in a broad range of demand models. |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:3865&r=all |
| By: | Xinyang Wang |
| Abstract: | If agents cooperate only within small groups of some bounded sizes, is there a way to partition the population into small groups such that no collection of agents can do better by forming a new group? This paper revisited f-core in a transferable utility setting. By providing a new formulation to the problem, we built up a link between f-core and the transportation theory. Such a link helps us to establish an exact existence result, and a characterization result of f-core for a general class of agents, as well as some improvements in computing the f-core in the finite type case. |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2005.11244&r=all |
| By: | Francisco Salas-Molina; Juan Antonio Rodr\'iguez Aguilar; Filippo Bistaffa |
| Abstract: | The concept of shared value was introduced by Porter and Kramer as a new conception of capitalism. Shared value describes the strategy of organizations that simultaneously enhance their competitiveness and the social conditions of related stakeholders such as employees, suppliers and the natural environment. The idea has generated strong interest, but also some controversy due to a lack of a precise definition, measurement techniques and difficulties to connect theory to practice. We overcome these drawbacks by proposing an economic framework based on three key aspects: coalition formation, sustainability and consistency, meaning that conclusions can be tested by means of logical deductions and empirical applications. The presence of multiple agents to create shared value and the optimization of both social and economic criteria in decision making represent the core of our quantitative definition of shared value. We also show how economic models can be characterized as shared value models by means of logical deductions. Summarizing, our proposal builds on the foundations of shared value to improve its understanding and to facilitate the suggestion of economic hypotheses, hence accommodating the concept of shared value within modern economic theory. |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2006.00581&r=all |