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on Game Theory |
| By: | Juang, W-T.; Sabourian, H. |
| Abstract: | For any game, we provide a justification for why in the long-run outcomes are mostly both efficient and egalitarian/symmetric in the Rawlsian sense. We do this by constructing an adaptive dynamic framework with four features. First, agents select rules to implement actions. Second, rule selection satisfies some minimal payoff monotonicity: rules that do best are chosen with a positive probability. Third, in choosing rules agents are subject to "small" random mutation. Fourth mutation is payoff-dependent with agents mutating more when they do badly than when they do well. Our main result is: if the set of feasible rules R is sufficiently rich then outcomes that survive maximise the payoff of the player that does least well. We also show that if R is restricted to those that do best-reply on uniform histories then outcomes that survive are efficient and egalitarian amongst the set of minimum weak CURB sets. Finally, we consider long-run outcomes assuming mutation is payoff-independent; in contrast to our strong selection result above, in this case we show indeterminacy: any outcome can survive if R is sufficiently rich. |
| JEL: | C70 C72 C73 |
| Date: | 2021–01–04 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2101&r=all |
| By: | Galit Ashkenazi-Golan (School of Mathematical Sciences [Tel Aviv] - Raymond and Beverly Sackler Faculty of Exact Sciences - Tel Aviv University [Tel Aviv]); Yevgeny Tsodikovich (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); Yannick Viossat (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | A common practice in many auctions is to offer bidders an opportunity to improve their bids, known as a Best and Final Offer (BAFO) stage. This final bid can depend on new information provided about either the asset or the competitors. This paper examines the effects of new information regarding competitors, seeking to determine what information the auctioneer should provide assuming the set of allowable bids is discrete. The rational strategy profile that maximizes the revenue of the auctioneer is the one where each bidder makes the highest possible bid that is lower than his valuation of the item. This strategy profile is an equilibrium for a large enough number of bidders, regardless of the information released. We compare the number of bidders needed for this profile to be an equilibrium under different information settings. We find that it becomes an equilibrium with fewer bidders when no additional information is made available to the bidders compared to when information regarding the competition is available. As a result, from the auctioneer's revenue perspective, when the number of bidders is unknown, there are some advantages to not revealing information between the stages of the auction. |
| Keywords: | auctions,multistage auctions,BAFO,information utilization |
| Date: | 2020–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-03078811&r=all |
| By: | Torsten Heinrich; Yoojin Jang; Luca Mungo; Marco Pangallo; Alex Scott; Bassel Tarbush; Samuel Wiese |
| Abstract: | We show that the playing sequence--the order in which players update their actions--is a crucial determinant of whether the best-response dynamic converges to a Nash equilibrium. Specifically, we analyze the probability that the best-response dynamic converges to a pure Nash equilibrium in random $n$-player $m$-action games under three distinct playing sequences: clockwork sequences (players take turns according to a fixed cyclic order), random sequences, and simultaneous updating by all players. We analytically characterize the convergence properties of the clockwork sequence best-response dynamic. Our key asymptotic result is that this dynamic almost never converges to a pure Nash equilibrium when $n$ and $m$ are large. By contrast, the random sequence best-response dynamic converges almost always to a pure Nash equilibrium when one exists and $n$ and $m$ are large. The clockwork best-response dynamic deserves particular attention: we show through simulation that, compared to random or simultaneous updating, its convergence properties are closest to those exhibited by three popular learning rules that have been calibrated to human game-playing in experiments (reinforcement learning, fictitious play, and replicator dynamics). |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2101.04222&r=all |
| By: | Gair, J. R.; Iyer, S.; Velu, C. |
| Abstract: | We examine a number of probabilistic choice models in which people might form their beliefs to play their strategies in a game theoretic setting in order to propose alternative equilibrium concepts to the Nash equilibrium. In particular, we evaluate the Blavatskyy model, Returns Based Beliefs (RBB) model, Quantal Response Equilibrium (QRE) model, Boundedly Rational Nash Equilibrium (BRNE) model and the Utility Proportional Beliefs (UPB) model. We outline the foundational axioms for these models and fully explicate them in terms of probabilistic actions, probabilistic beliefs and their epistemic characterizations. We test the model predictions using empirical data and show which models perform better under which conditions. We also extend the Blavatskyy model which was developed to consider games with two actions to cases where there are three or more actions. We provide a nuanced understanding of how different types of probabilistic choice models might predict better than others. |
| Keywords: | Subjective Probabilities, Decision Making, Cooperation |
| Date: | 2021–01–04 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2102&r=all |
| By: | Ambler, Kate; Jones, Kelly M.; Recalde, Maria P. |
| Abstract: | We study the validity of experimental methods designed to measure preferences for intra-household resource control among spouses in Ghana and Uganda. We implement two incentivized tasks; (1) a game that measures willingness to pay to control resources, and (2) private and joint dictator games that measure preferences for resource allocation and the extent to which those preferences are reflected in joint decisions. Behavior in the two tasks is correlated, suggesting that they describe similar underlying latent variables. In Uganda the experimental measures are robustly correlated with a range of household survey measures of resource control and women’s empowerment and suggest that simple private dictator games may be as informative as more sophisticated tasks. In Ghana, the experimental measures are not predictive of survey indicators, suggesting that context may be an important element of whether experimental measures are informative. |
| Keywords: | GHANA; WEST AFRICA; AFRICA SOUTH OF SAHARA; AFRICA; UGANDA; EAST AFRICA; empowerment; gender; women; women's empowerment; bargaining power; field experimentation; decision making; households; intra-household resource control; lab-in-the-field experiment |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:fpr:ifprid:1984&r=all |
| By: | Sarah Spycher; Ralph Winkler |
| Abstract: | We reassess the well-known “narrow-but-deep” versus “broad-but-shallow” trade-off in international environmental agreements (IEAs), taking into account the principal-agent relationship induced by the hierarchical structure of international policy. To this end, we expand the modest coalition formation game, in which countries first decide on whether to join an agreement and then decide on emissions by a strategic delegation stage. In the weak delegation game, principals first decide whether to join an IEA, then delegate the domestic emission choices to an agent. Finally, agents in all countries decide on emissions. In countries not joining the IEA, agents choose emissions to maximize their own payoff, while agents of countries joining the IEA set emissions to internalize some exogenously given fraction of the externalities that own emissions cause on all members of the IEA. In the strong delegation game principals first delegate to agents, which then decide on membership and emissions. We find that strategic delegation crowds out all efforts to increase coalition sizes by less ambitious agreements in the weak delegation game, while in the strong delegation game the first-best from the principals’ point of view can be achieved. |
| Keywords: | international climate policy, coalition formation game, political economy, strategic delegation, strategic voting |
| JEL: | Q54 Q58 C72 D62 H41 P16 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8769&r=all |
| By: | Biung-Ghi Ju (Department of Economics, Seoul National University); Min Kim (Rutgers University, USA); Suyi Kim (Hongik University, Korea); Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide;) |
| Abstract: | We study the design of fair international protocols for the abatement of GHG emissions. We formulate normative principles, pertaining to countries' population, emission history, and (business as usual) future emissions, as axioms for allocation rules. We show that combinations of these axioms characterize the so-called equal per capita allocation rules, with or without historical accountability. The allocations provided by these rules are in stark contrast with the allocation suggested by the Kyoto protocol, which is close to the allocation in proportion to the current and business-as-usual emissions, suggested by the equal per emission (grandfathering) rule. As we illustrate, equal per capita allocations admit more emissions to developing countries with large populations. And, with historical accountability, developed countries with large historical emissions are clearly penalized. |
| Keywords: | climate change; GHG reduction targets; allocation rules; historical accountability; history independence; equal per capita allocation |
| JEL: | D63 Q52 Q54 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:pab:wpaper:21.01&r=all |
| By: | Bergantino, Angela Stefania; Morone, Andrea; Gil Gallen, Sara |
| Abstract: | We investigate the effect of intragroup competition and risky marginal per capita returns on subjects' cooperative behavior in a one-shot public good game – following the wellknown approach proposed by Fischbacher, Gächter, and Fehr (2001) and extending the Colasante et al. (2019) and Colasante et al. (2018) parametrization. We are aiming to study the interaction between environment and social preferences and test the existence of a causal relationship of risk and competition over cooperative behavior when an individual’s benefit of the public good is heterogeneous and uncertain. Our results report experimental evidence about competition fostering cooperative behavior leading a raise contribution for all the subjects regardless of their social preferences. On the contrary, risky has a detrimental effect on cooperative behavior due to encouraging free riding. |
| Keywords: | risk; competition; conditional cooperator; marginal per capita return. |
| JEL: | C72 C92 D80 H41 |
| Date: | 2020–12–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:104465&r=all |
| By: | Rama Cont (LPSM UMR 8001 - Laboratoire de Probabilités, Statistiques et Modélisations - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, MI - Mathematical Institute [Oxford] - University of Oxford [Oxford]); Xin Guo (University of California [Berkeley] - University of California); Renyuan Xu (MI - Mathematical Institute [Oxford] - University of Oxford [Oxford]) |
| Abstract: | We study a class of N-player stochastic differential games of singular control, motivated by the study of a dynamic model of interbank lending with benchmark rates. We describe Pareto optima for this game and show how they may be achieved through the intervention of a regulator, whose policy is a solution to a singular stochastic control problem. Pareto optima are characterized in terms of the solution to a new class of Skorokhod problems with piecewise-continuous free boundary. Pareto optimal policies are shown to correspond to the enforcement of endogenous bounds on interbank lending rates. Analytical comparison between Pareto optima and Nash equilibria for the case of two players allows to quantify the impact of regulatory intervention on the stability of the interbank rate. |
| Keywords: | singular stochastic control,interbank markets,stochastic differential game,stochastic control,Pareto optimum,Nash equilibrium,Skorokhod problem,LIBOR rate,mathematical finance |
| Date: | 2020–12–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03049246&r=all |
| By: | Bos, Iwan; Marini, Marco A. |
| Abstract: | This paper analyzes price collusion in a repeated game with two submarkets; a standard and a premium quality segment. Within this setting, we study four types of price-fixing agreement: (i) a segment-wide cartel in the premium submarket only, (ii) a segment-wide cartel in the standard submarket only, (iii) two segment-wide cartels, and (iv) an industry-wide cartel. We present a complete characterization of the collusive pricing equilibrium and examine the corresponding effect on market shares and welfare. Partial cartels operating in a sufficiently large segment lose market share and the industry-wide cartel prefers to maintain market shares at pre-collusive levels. The impact on consumer and social welfare critically depends on the cost of producing quality. Moreover, given that there is a cartel, more collusion can be beneficial for society as a whole. |
| Keywords: | Demand and Price Analysis |
| Date: | 2020–12–16 |
| URL: | http://d.repec.org/n?u=RePEc:ags:feemgc:307986&r=all |
| By: | Bergantiños, Gustavo; Moreno-Ternero, Juan D. |
| Abstract: | We study the sharing of revenues raised from the collective sale of broadcasting rights for La Liga, which is strongly regulated by the Spanish government since 2015. Regulation imposes, somewhat surprisingly, that lower bounds and performance measures outweigh the capability (of each club) to generate resources from selling broadcasting rights. Also, more disturbingly, the latter dimension cannot be rationalized by a sharing rule with solid normative grounds. |
| Keywords: | La Liga, broadcasting rights, sport leagues, resource allocation |
| JEL: | C71 |
| Date: | 2020–12–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:104750&r=all |