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on Game Theory |
| By: | Heinrich H. Nax; Bary S. R. Pradelski |
| Abstract: | We study evolutionary dynamics in assignment games where many agents interact anonymously at virtually no cost. The process is decentralized, very little information is available and trade takes place at many different prices simultaneously. We propose a completely uncoupled learning process that selects a subset of the core of the game with a natural equity interpretation. This happens even though agents have no knowledge of other agents’ strategies, payoffs, or the structure of the game, and there is no central authority with such knowledge either. In our model, agents randomly encounter other agents, make bids and offers for potential partnerships and match if the partnerships are profitable. Equity is favored by our dynamics because it is more stable, not because of any ex ante fairness criterion. |
| Keywords: | assignment games; cooperative games; core; equity; evolutionary game theory; learning; matching markets; stochastic stability |
| JEL: | C71 C73 C78 D8 D83 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:65428&r=gth |
| By: | Meinhardt, Holger Ingmar |
| Abstract: | Nguyen and Thomas (2016) claimed that they have found a method to compute the nucleoli of games with more than 50 players using nested linear programs (LP). Unfortunately, this claim is false. They incorrectly applied the indirect proof by ``A and not B implies A and not A'' to conclude that ``if A then B''is valid. In fact, they prove that a truth implies a falsehood. As established by Meinhardt (2015a), this is a wrong statement. Therefore, instead of giving a proof of their main Theorem 4b, they give a disproof. It comes as no surprise to us that the flow game example presented by these authors to support their arguments is obviously a counter-example of their algorithm. We show that the computed solution by this algorithm is neither the nucleolus nor a core element of the flow game. Moreover, the stopping criterion of all proposed methods is wrong, since it does not satisfy one of Kohlberg's properties (cf. Kohlberg (1971)). As a consequence, none of these algorithms is robust. |
| Keywords: | Transferable Utility Game, Nucleolus, Flow Problem, Propositional Logic; Circular Reasoning (circulus in probando); Indirect Proof; Proof by Contradiction; Proof by Contraposition. |
| JEL: | C71 |
| Date: | 2016–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69789&r=gth |
| By: | Heinrich H. Nax; Ryan O. Murphy; Dirk Helbing |
| Abstract: | We study the stability and welfare properties of merit-based (meritocratic) group-matching mechanisms in voluntary contribution games. Meritocratic matching in this context means that players tend to be assortatively grouped according to their contributions. We let regimes di ffer from one another with respect to their matching fidelity. The stability analysis summarizes as follows. When there is not enough meritocracy, the only equilibrium state is universal free-riding. Above a first threshold, several Nash equilibria above free-riding emerge, but only the free-riding equilibrium is stochastically stable. There exists a second meritocratic threshold, above which an equilibrium with high contributions becomes the unique stochastically stable state. This operationalization of meritocracy sheds light on critical transitions, that are enabled by contribution-assortative matching, between equilibria related to "tragedy of the commons |
| Keywords: | meritocracy; voluntary contribution; public goods; stochastic stability; evolutionary stability; assortative matching; welfare; efficiency-equality tradeoff |
| JEL: | C73 D02 D63 |
| Date: | 2014–10–21 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:65444&r=gth |
| By: | Christian Basteck (Technische Universitaet Berlin) |
| Abstract: | We characterize voting procedures according to the solution that they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In the larger class of direct mechanism scoring rules, Approval Voting is characterized by a single axiom – it is majoritarian after eliminating a Pareto dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected). However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). Finally, there exists no direct mechanism scoring rule that satisfies both MEPD and MON or Condorcet consistency (CON). |
| Keywords: | Sophisticated Voting; Iterated Weak Dominance; Implementation; Plurality Rule; Borda Rule; Approval Voting |
| JEL: | C72 D71 D72 |
| Date: | 2016–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:bdp:wpaper:2016002&r=gth |
| By: | Ludovic Alexandre Julien |
| Abstract: | In this paper, we provide new proofs of existence and uniqueness of a Stackelberg market equilibrium for a multiple leader-follower noncooperative oligopoly model in which heterogeneous firms compete on quantities. To this end, we consider a two-step game of perfect and complete information in which many leaders interact strategically with many followers. The Stackelberg market equilibrium constitutes a pure strategy subgame perfect Nash equilibrium of this game. The existence (and uniqueness) problem is complexified in this framework since strategic interactions occur within each partial game but also between both partial games through sequential decisions. Then, to prove existence, we notably provide a new procedure to determine (the conditions under which) the optimal behavior of the followers (may be written) as functions of the leaders'strategy profile only. Some examples outline our procedure and discuss our assumptions. |
| Keywords: | Best response functions, existence, uniqueness. |
| JEL: | D43 L13 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:drm:wpaper:2016-13&r=gth |
| By: | Akira Okada (Kyoto University); Ryoji Sawa (University of Aizu) |
| Abstract: | This paper considers a dynamic process of n-person social choice problems under q-majority where a status-quo policy is challenged by an opposing policy drawn randomly in each period. The opposing policy becomes the next status-quo if it receives at least q votes. We characterize stochastically stable policies under a boundedly rational choice rule of voters. Under the best response rule with mutations, a Condorcet winner is stochastically stable for all q-quota rules, and uniquely so if q is greater than the minmax quota. Under the logit choice rule, the Borda winner is stochastically stable under the unanimity rule. Our evolutionary approach provides a dynamic foundation of the mini-max policies in multidimensional choice problems with Euclidean preferences. |
| Keywords: | Stochastic stability; Social choice; Voting; Condorcet winner. |
| JEL: | C71 C73 D71 |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:936&r=gth |
| By: | Peters H.J.M.; Schröder M.J.W.; Vermeulen A.J. (GSBE) |
| Abstract: | We consider a variant of Hotellings location model that was proposed by Kohlberg 1983 when choosing a firm, consumers take travel time and also expected waiting time, which again depends on the number of consumers choosing that firm, into consideration. If we assume that firms are symmetric, then we show that a subgame perfect equilibrium exists if there is an even, but small, number of firms and no subgame perfect equilibrium exists if there is an odd, but small, number of firms. Further, we illustrate by means of examples what other subgame perfect equilibria exist if we allow for asymmetric firms. |
| Keywords: | Noncooperative Games; Market Structure and Pricing: Oligopoly and Other Forms of Market Imperfection; Real Estate Markets, Production Analysis, and Firm Location: General; |
| JEL: | C72 D43 R30 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2015040&r=gth |
| By: | Gabszewicz, J.J. (Université catholique de Louvain, CORE, Belgium); Marini, M. (University of Rome La Sapienza); Tarola, O. (University of Rome La Sapienza) |
| Abstract: | This paper studies how the possibility for firms to sign collusive agreements (as for instance being part of alliances, cartels and mergers) may affect their quality and price choice in a market with vertically differentiated goods. For this purpose we model the firm decisions as a three-stage game in which, at the first stage, firms can form an alliance via a sequential game of coalition formation and, at the second and third stage, they decide simultaneously their product qualities and prices, respectively. In such a setting we study whether there exist circumstances under which either full or partial collusion can be sustained as a subgame perfect Nash equilibrium of the coalition formation game. Also, we analyse the effects of different coalition structures on equilibrium qualities, prices and profits accruing to firms. It is shown that only intermediate coalition structures arise at the equilibrium, with the bottom quality firm always included. Moreover, all equilibrium price and quality configurations always coincide with that observed in the duopoly case, with only two quality variants on sale. |
| Keywords: | Vertically differentiated market, endogenous alliance formation, coalition structures, price collusion, grand coalition, coalition stability, sequential games of coalition formation |
| JEL: | D42 D43 L1 L12 L13 L41 |
| Date: | 2015–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2015030&r=gth |
| By: | Oscar Volij (BGU); Casilda Lasso de la Vega (University of the Basque Country) |
| Keywords: | Matches, stochastic games, recursive games |
| JEL: | C72 C73 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:bgu:wpaper:1601&r=gth |
| By: | Sean HORAN |
| Abstract: | Despite the wide range of agendas used in legislative decision-making, the literature has focused almost exclusively on two stylized formats, the so-called Euro-Latin and Anglo-American agendas. As emphasized by Ordeshook and Schwartz [1987], this focus leaves a sizable gap in our understanding of the legislative process. To help address the deficiency, I first define a very broad class of agendas (called simple agendas) whose features are common among agendas used in legislative settings. I then characterize the sophisticated (Farquharson [1969]) voting outcomes implemented by agendas in this class. By establishing a clear connection between the structure of simple agendas and the outcomes associated with them, the characterization extends our understanding of legislative decision-making well beyond the very limited scope of Euro-Latin and Anglo-American agendas. |
| Keywords: | majority voting, sophisticated voting, agendas, committees, implementation |
| JEL: | C72 D02 D71 D72 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montec:02-2016&r=gth |
| By: | Kim, Chulyoung |
| Abstract: | The legal community has been debating the question of who should select and provide expert witnesses at trial: the litigant or the judge? Using a persuasion-game framework, I show that there is a trade-off. On the one hand, the litigant is willing to consult an expert even when the judge is reluctant to appoint her own experts due to high costs. On the other hand, given the same amount of expert advice, the judge can make a more accurate decision when using a court-appointed expert's advice at trial. I show that the cost of expert advice is an important factor in this trade-off and, therefore, in the argument for the reform toward a centralized system for expert witnesses. |
| Keywords: | expert witnesses, decentralized institution, centralized institution, persuasion game, evidence distortion |
| JEL: | C72 D82 K41 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69618&r=gth |
| By: | E. Roy Weintraub |
| Abstract: | This essay reviews new histories of the role of game theory and rational decision-making in shaping the social sciences, economics among them, in the post war period. The recent books The World the Game Theorists Made by Paul Erickson and How Reason Almost Lost Its Mind by Paul Erickson, Judy Klein, Lorraine Daston, Rebecca Lemov, Thomas Sturm, and Michael Gordin raise a number of complex historical questions about the interconnections among game theory, utility theory, decision-theory, optimization theory, information theory and theories of rational choice. Moreover the contingencies of time, place, and person call into question the usefulness of economists’ linear narratives about the autonomous and progressive development of modern economics. The essay finally reflects on the challenges that these issues present for historians of recent economics. |
| Keywords: | game theory, rational choice |
| JEL: | A11 A12 B2 C02 C6 C7 D01 D7 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:hec:heccee:2016-19&r=gth |
| By: | Brams, Steven J.; Ismail, Mehmet S. |
| Abstract: | The rules of many sports are not fair—they do not ensure that equally skilled competitors have the same probability of winning. As an example, the penalty shootout in soccer, wherein a coin toss determines which team kicks first on all five penalty kicks, gives a substantial advantage to the first-kicking team, both in theory and practice. We show that a so-called Catch-Up Rule for determining the order of kicking would not only make the shootout fairer but also is essentially strategyproof. By contrast, the so-called Standard Rule now used for the tiebreaker in tennis is fair. We briefly consider several other sports, all of which involve scoring a sufficient number of points to win, and show how they could benefit from certain rule changes, which would be straightforward to implement. |
| Keywords: | Sports rules, fairness, strategyproofness, Markov process, soccer, tennis |
| JEL: | C6 C61 C7 D6 D63 |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69714&r=gth |
| By: | Alejandra Catalina Parra Ochoa |
| Abstract: | En el presente trabajo se realizó un estudio del mercado eléctrico colombiano enfocado al cargo por confiabilidad y, en especial, al mecanismo de subastas empleado para la asignación del mismo. El trabajo se divide en cinco partes, en la primera parte se realiza una descripción detallada del funcionamiento del mercado eléctrico en Colombia, en la segunda parte, una descripción del cargo por confiabilidad, en la tercera, una revisión de los mecanismos de asignación del cargo por confiabilidad en Colombia, en la cuarta, un análisis de las fallas presentadas por el mecanismo en el año 2015 y, finalmente, en la quinta parte se exponen las conclusiones obtenidas. |
| Keywords: | subastas, mercado eléctrico, cargo por confiabilidad, energía firme, servicio. |
| JEL: | C79 D82 H41 L51 L94 |
| Date: | 2015–12–30 |
| URL: | http://d.repec.org/n?u=RePEc:col:000176:014240&r=gth |
| By: | Hindriks, J. (Université catholique de Louvain, CORE, Belgium); Nishimura, Y. (Osaka University) |
| Abstract: | This paper reconciles two opposite results in the tax competition literature. On one side Kempf and Rota-Graziosi (J.Pub. Econ 94:768-776, 2010) and Hindriks and Nishimura (J. Pub Econ 121:66-68, 2015) have shown that the two Stackelberg outcomes prevail as the subgame perfect equilibria when capital is entirely owned by non-residents. On the other side Ogawa (Int. Tax Pub Fin 20:474-484, 2013) has shown that the simultaneous- move outcome prevails when capital is entirely owned by residents. We develop a model in which capital ownership can vary freely between these two polar cases. We show that there exists a unique degree of residential capital ownership such that the equilibrium switches from the Stackelberg to the simultaneous-move outcomes. The chance for the simultaneous-move outcome to prevail increases with the extent of asymmetry among regions. |
| Keywords: | Endogenous timing; Tax competition; Capital ownership |
| JEL: | H30 H87 C72 |
| Date: | 2015–05–31 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2015021&r=gth |