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on Game Theory |
| By: | Peter A. Streufert |
| Abstract: | This paper develops the category $\mathbf{NCG}$. Its objects are node-and-choice games, which include essentially all extensive-form games. Its morphisms allow arbitrary transformations of a game's nodes, choices, and players, as well as monotonic transformations of the utility functions of the game's players. Among the morphisms are subgame inclusions. Several characterizations and numerous properties of the isomorphisms are derived. Also, the game-theoretic concepts of no-absentmindedness, perfect-information, and (pure-strategy) Nash-equilibrium are shown to be isomorphically invariant. Finally, full subcategories are defined for choice-sequence games and choice-set games, and relationships among these two subcategories and $\mathbf{NCG}$ itself are expressed and derived via isomorphic inclusions and equivalences. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.11196&r=all |
| By: | Soham R. Phade; Venkat Anantharam |
| Abstract: | The betweenness property of preference relations states that a probability mixture of two lotteries should lie between them in preference. It is a weakened form of the independence property and hence satisfied in expected utility theory (EUT). Experimental violations of betweenness are well-documented and several preference theories, notably cumulative prospect theory (CPT), do not satisfy betweenness. We prove that CPT preferences satisfy betweenness if and only if they conform with EUT preferences. In game theory, lack of betweenness in the players' preference relations makes it essential to distinguish between the two interpretations of a mixed action by a player - conscious randomizations by the player and the uncertainty in the beliefs of the opponents. We elaborate on this distinction and study its implication for the definition of Nash equilibrium. This results in four different notions of equilibrium, with pure and mixed action Nash equilibrium being two of them. We dub the other two pure and mixed black-box strategy Nash equilibrium respectively. We resolve the issue of existence of such equilibria and examine how these different notions of equilibrium compare with each other. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.09592&r=all |
| By: | Niko Jaakkola (University of Bologna); Florian Wagener (University of Amsterdam) |
| Abstract: | We characterise the entire set of symmetric stationary Markov-perfect Nash equilibria (MPE) in a differential game of public good investment, using the canonical problem of climate change as an example. We provide a sufficient and necessary condition for MPE and show how the entire set of MPE is constructed. The equilibrium in continuous strategies, unique in our context, is Pareto-dominated by any other equilibrium. If a Pareto- undominated steady state exists, it is sustained by trigger-like strategies, with deviations above and below the steady state leading to different re- sponses. We extend the theory of differential games to deal with payoffs under discontinuous strategies. Our methods work under general functional forms. |
| JEL: | C73 Q54 |
| Date: | 2020–04–20 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20200020&r=all |
| By: | Stefan Penczynski (School of Economics and CBESS, University of East Anglia, Norwich.); Stefania Sitzia (School of Economics and CBESS, University of East Angle, Norwich.); Jiwei Zheng (School of Economics and CBESS, University of East Anglia, Norwich.) |
| Abstract: | This study introduces the game theoretical concept of “compound games†and investigates whether the decomposition of a game influences behaviour. Specifically, we investigate whether separating battle of the sexes games into a pure coordination component and the remaining battle of the sexes component changes coordination success. The literature attributes high coordination rates in pure coordination games with focal points to team reasoning and low coordination rates in related battle of the sexes games to level-k reasoning. We find that coordination success in compound games depends on the decomposition and order of component games, suggesting that collective interests are fragile in the presence of opposing individual interests. Our results show that compound games are empirically relevant; we discuss a wide range of possible applications for compound games. |
| Keywords: | Compound games, focal points, framing, collective interest |
| JEL: | C72 C91 D90 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:uea:wcbess:20-04&r=all |
| By: | Olivier de Mouzon (TSE - Toulouse School of Economics - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - UT1 - Université Toulouse 1 Capitole - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Thibault Laurent (TSE - Toulouse School of Economics - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - UT1 - Université Toulouse 1 Capitole - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Michel Le Breton (TSE - Toulouse School of Economics - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - UT1 - Université Toulouse 1 Capitole - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Dominique Lepelley (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion) |
| Keywords: | Electoral system,Election Inversions,Impartial Anonymous Culture |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-02547744&r=all |
| By: | Stefano Dughera (EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique, Department of Economics and Statistics Cognetti de Martiis, University of Torino, Collegio Carlo Alberto); Alain Marciano (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier, Université de Montpellier) |
| Abstract: | The goal of this paper is to study the consequences of non-reciprocal or unilateral altruism, that is, of altruism between individuals who have different concern for others. By contrast to what the literature usually shows-that unilateral altruists lead egoists to cooperate, that non-reciprocal altruism destroys altruism or that it generates non-desirable exploitation-we show that unilateral altruism does not forcedly lead egoists to cooperate nor it destroys altruism and that, in some situations, it can even be Pareto improving. By analyzing a simple cooperation game with other-regarding preferences, we find that unilateral altruism gives birth to a Samaritan's Dilemma where egoists predate Samaritans by free-riding on their contribution. Perhaps counterintuitively, we also show that in case "exploited" Samaritans experience a higher subjective well-being than in a classical Prisoners' dilemma. Finally, we derive conditions for the evolutionary stability of both the predators' and Samaritans' behavior. |
| Keywords: | altruism,cooperation,predation,exploitation,Samaritan's dilemma,evolutionary game theory JEL Codes C73 H41 D64 D74 |
| Date: | 2020–04–22 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02550432&r=all |
| By: | Cary Deck (University of Alabama); Lance Howe (University of Alaska Anchorage); Matthew Reimer (University of Alaska Anchorage); Jonathan Alevy (University of Alaska Anchorage); Kyle Borash (University of Alaska Anchorage) |
| Abstract: | The process of allocating rights to resources can be viewed as a contest: parties compete with each other for the right to claim a larger allocation. In some situations, the amount of the resource that is available to allocate may be unknown when parties are competing for shares and perhaps not realized until contestants actually attempt to claim their shares of the resource. For example, fishing quotas may be awarded based on estimated fish populations, but if there are fewer fish than anticipated, those who are last to harvest may not be able to fill their quota. We model contests of this form and test the predictions of the model using a controlled laboratory experiment. The general result is that participants compete less intensively for shares of the resource when uncertainty regarding the size of the prize is resolved later in the process. |
| Keywords: | Contests with Uncertain Prizes, Fisheries, Experimental Economics |
| JEL: | C7 C9 D7 Q2 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:ala:wpaper:2020-02&r=all |
| By: | Martin Bodenstein; Giancarlo Corsetti; Luca Guerrieri |
| Abstract: | The consensus in the recent literature is that the gains from international monetary cooperation are negligible, and so are the costs of a breakdown in cooperation. However, when assessed conditionally on empirically-relevant dynamic developments of the economy, the welfare cost of moving away from regimes of explicit or implicit cooperation may rise to multiple times the cost of economic fluctuations. In economies with incomplete markets, the incentives to act non-cooperatively are driven by the emergence of global imbalances, i.e., large net-foreign-asset positions; and, in economies with complete markets, by divergent real wages. |
| Keywords: | Monetary policy cooperation; Global imbalances; Open-loop Nash games |
| JEL: | E44 E61 F42 |
| Date: | 2020–02–25 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgif:1271&r=all |
| By: | Frederic Chantreuil (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, LARJE - Laboratoire de Recherches Juridique et Economique - UNC - Université de la Nouvelle Calédonie, TEPP - Travail, Emploi et Politiques Publiques - UPEM - Université Paris-Est Marne-la-Vallée - CNRS - Centre National de la Recherche Scientifique); Kévin Fourrey (TEPP - Travail, Emploi et Politiques Publiques - UPEM - Université Paris-Est Marne-la-Vallée - CNRS - Centre National de la Recherche Scientifique, LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM], CEET - Centre d'études de l'emploi et du travail - CNAM - Conservatoire National des Arts et Métiers [CNAM] - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche - Ministère du Travail, de l'Emploi et de la Santé); Thérèse Rebière (IZA Bonn, LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM], CEET - Centre d'études de l'emploi et du travail - CNAM - Conservatoire National des Arts et Métiers [CNAM] - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche - Ministère du Travail, de l'Emploi et de la Santé, TEPP - Travail, Emploi et Politiques Publiques - UPEM - Université Paris-Est Marne-la-Vallée - CNRS - Centre National de la Recherche Scientifique); Isabelle Lebon (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, TEPP - Travail, Emploi et Politiques Publiques - UPEM - Université Paris-Est Marne-la-Vallée - CNRS - Centre National de la Recherche Scientifique) |
| Date: | 2020–04–23 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02552244&r=all |
| By: | Marvin Deversi; Martin G. Kocher; Christiane Schwieren |
| Abstract: | We analyze cooperation within a company setting in order to study the relationship between cooperative attitudes and financial as well as non-financial rewards. In total, 910 employees of a large software company participate in an incentivized online experiment. We observe high levels of cooperation and the typical conditional contribution patterns in a modified public goods game. When linking experiment and company record data, we observe that cooperative attitudes of employees do not pay off in terms of financial rewards within the company. Rather, cooperative employees receive non-financial benefits such as recognition or friendship as the main reward medium. In contrast to most studies in the experimental laboratory, sustained levels of cooperation in our company setting relate to non-financial values of cooperation rather than solely to financial incentives. |
| Keywords: | cooperation, social dilemma, field experiment, company |
| JEL: | C93 D23 H41 J31 J32 M52 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8190&r=all |
| By: | Alger, Ingela |
| Abstract: | Why are some societies monogamous and others polygynous? Most theories of polygyny in-voke male heterogeneity as an explanation. Arguing that such heterogeneity depends on men’swillingness to compete against each other in the first place, I propose an evolutionary gameto model the evolution of this trait. Lack of competitiveness (and the associated monogamousunions) is shown to be compatible with evolution if male reproductive success decreases withthe number of wives. In a model where the man and his spouse(s) make fertility and child carechoices that aim at maximizing reproductive success, I show that, due to men’s involvement inchild care and female agency over her fertility, male reproductive success is decreasing in thenumber of wives under certain conditions and increasing in others. The model thus sheds lighton the variation in polygyny rates across space and time in human societies. |
| JEL: | D13 C73 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:tse:iastwp:124215&r=all |
| By: | Charles Bertucci (CMAP, Ecole Polytechnique, Palaiseau, France); Louis Bertucci (Institut Louis Bachelier, Paris, France; Haas School of Business, UC Berkeley, Berkeley, California); Jean-Michel Lasry (Universit\'e Paris-Dauphine, PSL Research University, CEREMADE, Paris, France); Pierre-Louis Lions (Universit\'e Paris-Dauphine, PSL Research University, CEREMADE, Paris, France; Coll\`ege de France, Paris, France) |
| Abstract: | We present an analysis of the Proof-of-Work consensus algorithm, used on the Bitcoin blockchain, using a Mean Field Game framework. Using a master equation, we provide an equilibrium characterization of the total computational power devoted to mining the blockchain (hashrate). From a simple setting we show how the master equation approach allows us to enrich the model by relaxing most of the simplifying assumptions. The essential structure of the game is preserved across all the enrichments. In deterministic settings, the hashrate ultimately reaches a steady state in which it increases at the rate of technological progress. In stochastic settings, there exists a target for the hashrate for every possible random state. As a consequence, we show that in equilibrium the security of the underlying blockchain is either $i)$ constant, or $ii)$ increases with the demand for the underlying cryptocurrency. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.08167&r=all |