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on Game Theory |
| By: | Sam Ganzfried |
| Abstract: | The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may obtain an extremely low payoff. On the other hand, a maximin strategy assumes that all opposing agents are playing to minimize our payoff (even if it is not in their best interest), and ensures the maximal possible worst-case payoff, but results in exceedingly conservative play. We propose a new solution concept called safe equilibrium that models opponents as behaving rationally with a specified probability and behaving potentially arbitrarily with the remaining probability. We prove that a safe equilibrium exists in all strategic-form games (for all possible values of the rationality parameters), and prove that its computation is PPAD-hard. We present exact algorithms for computing a safe equilibrium in both 2 and $n$-player games, as well as scalable approximation algorithms. |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2201.04266&r= |
| By: | Cary D. Frydman; Salvatore Nunnari |
| Abstract: | We propose and experimentally test a theory of strategic behavior in which players are cognitively imprecise and perceive a fundamental parameter with noise. We focus on 2 x 2 coordination games, which generate multiple equilibria when perception is precise. When adding a small amount of cognitive imprecision to the model, we obtain a unique equilibrium where players use a simple cutoff strategy. The model further predicts that behavior is context-dependent: players implement the unique equilibrium strategy with noise, and the noise decreases in fundamental volatility. Our experimental data strongly support this novel prediction and reject several alterna-tive game-theoretic models that do not predict context-dependence. We also find that subjects are aware of other players’ imprecision, which is key to generating strategic uncertainty. Our framework has important implications for the literature on global games and, more broadly, illuminates the role of perception in generating both random and context-dependent behavior in games. |
| Keywords: | perception, efficient coding, coordination, global games |
| JEL: | C72 C92 D91 E71 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9483&r= |
| By: | Guzman, Cristobal; Riffo, Javiera; Telha, Claudio; Van Vyve, Mathieu (Université catholique de Louvain, LIDAM/CORE, Belgium) |
| Abstract: | We introduce an inspection game where one inspector has the role ofmonitoring a group of inspectees. The inspector has the resources to visit only a few of them. Visits are performed sequentially with no repetitions. The inspectees report and share the sequence of inspections as they occur, but otherwise, they do not cooperate. Our paper focuses on the mathematical structure of the equilibria of this sequential inspection game, where the inspector can perform exactly two visits. We formulate two Stackelberg models, a static game where the inspector commits to play a sequence of visits announced at the start of the game, and a dynamic game where the second visit will depend on who was visited previously. In the static game, we characterize the (randomized) inspection paths in equilibrium using linear programs. In particular, these inspection paths are solutions to a transportation problem. We use this equivalence to determine an explicit solution to the game and to show that set of inspection path probabilities in equilibrium, projected onto its first and second visit marginals, is convex. In the dynamic game, we determine the inspection paths in equilibrium using backward induction. We discuss how the static and dynamic games relate to each other and how to use these models in practical settings. |
| Keywords: | Game Theory ; Inspection Games ; Sequential Stackelberg Games |
| Date: | 2021–12–03 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2021036&r= |
| By: | Bos, Iwan; Marini, Marco A.; Saulle, Riccardo |
| Abstract: | This paper examines capacity-constrained oligopoly pricing with sellers who seekmyopic improvements. We employ the Myopic Stable Set solution concept and establish the existence of a unique pure-strategy price solution for any given level of capacity. This solution is shown to coincide with the set of pure-strategy Nash equilibria when capacities are large or small. For an intermediate range of capacities, it predicts a price interval that includes the mixedstrategy support. This stability concept thus encompasses all Nash equilibria and offers a pure-strategy solution when there is none in Nash terms. It particularly provides a behavioral rationale for different pricing patterns, including Edgeworth price cycles and states of hyper-competition with supply shortages. We also analyze the impact of a change in firm size distribution. A merger among the biggest firms may lead to more price dispersion as it increases the maximum and decreases the minimum myopically stable price. |
| Keywords: | Bounded Rationality, Capacity Constraints, Mergers, Myopic Stable Set, Oligopoly Pricing, Supply Shortages |
| JEL: | C72 D43 L13 |
| Date: | 2021–12–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111176&r= |
| By: | Dehez, Pierre (Université catholique de Louvain, LIDAM/CORE, Belgium) |
| Abstract: | 1-convex games have been introduced by Theo Driessen in his 1985 PhD dissertation. They form an interesting class of games for at least one reason: the core of a 1-convex n-player game is a regular simplex of dimension n – 1 or a single point. As a consequence, its nucleolus is the center of gravity of the core. We recall and extend the results obtained by Driessen and provide examples and applications. |
| Keywords: | Transferable utility games ; core ; nucleolus ; Shapley value |
| JEL: | C71 |
| Date: | 2021–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2021016&r= |
| By: | Evan M. Calford; Anujit Chakraborty |
| Abstract: | Do experimental subjects have consistent first and higher-order beliefs about other’s preferences? How does any inconsistency affect strategic decisions? We introduce a simple four-player sequential social dilemma where actions reveal first and higher-order beliefs. The unique sub game perfect Nash equilibrium (SPNE) is observed less than 5% of the time, even though our diagnostic treatments show that a majority of our subjects are self-interested, higher-order rational and have accurate first-order beliefs. In our data, strategic play vastly deviates from Nash predictions because first-order and higher-order beliefs are inconsistent for most subjects. |
| Keywords: | Experimental economics, Higher-order beliefs, Social dilemma |
| JEL: | F02 F13 F15 |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2022-681&r= |
| By: | Xiaoliang Li |
| Abstract: | In this discussion draft, we explore different duopoly games of players with quadratic costs, where the market is supposed to have the isoelastic demand. Different from the usual approaches based on numerical computations, the methods used in the present work are built on symbolic computations, which can produce analytical and rigorous results. Our investigation shows that the stability regions are enlarged for the games considered in this work compared to their counterparts with linear costs. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.05948&r= |
| By: | Herings, P. Jean-Jacques; Mauleon, Ana (Université catholique de Louvain, LIDAM/CORE, Belgium); Vannetelbosch, Vincent (Université catholique de Louvain, LIDAM/CORE, Belgium) |
| Abstract: | We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other individuals but also about how a mediator is going to solve conflicts of interest. The set of socially rationalizable outcomes with mediation is shown to be non-empty for all social environments and it can be computed by an iterative reduction procedure. We show that social rationalizability with mediation does not necessarily satisfy coalitional rationality when the number of coalition members is greater than two. |
| Keywords: | Social environments ; rationalizability ; mediation ; coalitional rationality |
| JEL: | C70 C72 C78 |
| Date: | 2021–11–26 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2021017&r= |
| By: | Bernhard Kasberger; Kyle Woodward |
| Abstract: | We study multi-unit auctions in which bidders have limited knowledge of opponent strategies and values. We characterize optimal prior-free bids; these bids minimize the maximal loss in expected utility resulting from uncertainty surrounding opponent behavior. Optimal bids are simply computable despite bidders having multi-dimensional private information, and in certain cases admit closed-form solutions. In the pay-as-bid auction the minimax-loss bid is unique; in the uniform-price auction the minimax-loss bid is unique if the bidder is allowed to determine the quantities for which they bid, as in many practical applications. Payments to the seller may be higher in either auction format, but minimax-loss bids are never uniformly higher in the pay-as-bid auction. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.11320&r= |
| By: | Gächter, Simon (University of Nottingham); Lee, Kyeongtae (Bank of Korea); Sefton, Martin (University of Nottingham); Weber, Till O. (Newcastle University) |
| Abstract: | The prisoner's dilemma (PD) is arguably the most important model of social dilemmas, but our knowledge about how a PD's material payoff structure affects cooperation is incomplete. In this paper we investigate the effect of variation in material payoffs on cooperation, focussing on one-shot PD games where efficiency requires mutual cooperation. Following Mengel (2018) we vary three payoff indices. Indices of risk and temptation capture the unilateral incentives to defect against defectors and co-operators respectively, while an index of efficiency captures the gains from cooperation. We conduct two studies: first, varying the payoff indices over a large range and, second, in a novel orthogonal design that allows us to measure the effect of one payoff index while holding the others constant. In the second study we also compare a student and non-student subject pool, which allows us to assess generalizability of results. In both studies we find that temptation reduces cooperation. In neither study, nor in either subject pool of our second study, do we find a significant effect of risk. |
| Keywords: | prisoner’s dilemma, cooperation, temptation, risk, efficiency |
| JEL: | A13 C91 |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp14895&r= |
| By: | Kshitija Taywade; Brent Harrison; Adib Bagh |
| Abstract: | We investigate the use of a multi-agent multi-armed bandit (MA-MAB) setting for modeling repeated Cournot oligopoly games, where the firms acting as agents choose from the set of arms representing production quantity (a discrete value). Agents interact with separate and independent bandit problems. In this formulation, each agent makes sequential choices among arms to maximize its own reward. Agents do not have any information about the environment; they can only see their own rewards after taking an action. However, the market demand is a stationary function of total industry output, and random entry or exit from the market is not allowed. Given these assumptions, we found that an $\epsilon$-greedy approach offers a more viable learning mechanism than other traditional MAB approaches, as it does not require any additional knowledge of the system to operate. We also propose two novel approaches that take advantage of the ordered action space: $\epsilon$-greedy+HL and $\epsilon$-greedy+EL. These new approaches help firms to focus on more profitable actions by eliminating less profitable choices and hence are designed to optimize the exploration. We use computer simulations to study the emergence of various equilibria in the outcomes and do the empirical analysis of joint cumulative regrets. |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2201.01182&r= |
| By: | Masaaki Fujii (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo); Akihiko Takahashi (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo) |
| Abstract: | We study an equilibrium-based continuous asset pricing problem for the securities market. In the previous work [16], we have shown that a certain price process, which is given by the solution to a forward backward stochastic differential equation of conditional McKean-Vlasov type, asymptotically clears the market in the large population limit. In the current work, under suitable conditions, we show the existence of a finite agent equilibrium and its strong convergence to the corresponding mean-field limit given in [16]. As an important byproduct, we get the direct estimate on the difference of the equilibrium price between the two markets; the one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:cfi:fseres:cf529&r= |
| By: | Ludger Overbeck; Florian Schindler |
| Abstract: | We study two different contributions to the theory of systemic risk measures. It turns out, that crucial properties are shared by both types and that in most relevant cases both can be included in the axiomatic approach. Moreover, a capital allocation rule (CAR) in the spirit of Aumann-Shapley is introduced which gives us the opportunity to compute systemic capital allocations regardless of the risk measurement approach. Additionally, this CAR yields an alternative approach to find the corresponding counterpart in the axiomatic approach. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.06534&r= |
| By: | Catherine Bobtcheff (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - 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); Raphaël Levy (HEC Paris - Ecole des Hautes Etudes Commerciales); Thomas Mariotti (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Two players receiving independent signals on a risky project with common value compete to be the first to invest. We characterize the equilibrium of this preemption game as the publicity of signals varies. Private signals create a winner's curse: the first mover suspects that his rival might have privately received adverse information, hence exited. To compensate, players seek more evidence supporting the project, resulting in later investment. A conservative planner concerned with avoiding unprofitable investments may then prefer private signals. Our results suggest that policy interventions should primarily tackle winner-takes-all competition, and regulate transparency only once competition is sufficiently mild. |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:psewpa:halshs-03507030&r= |
| By: | Boris Ginzburg; José-Alberto Guerra |
| Abstract: | We study the implications of participation in political collective action on identity and on interpersonal interactions using a laboratory experiment. We offer subjects the possibility to sign an online petition, which was either related to animal rights or the right to bear firearms. Before and after the petition, we measure subjects' altruism and willingness to trust by asking them to play a dictator game and a trust game in pairs. The results show that there is considerably more altruism and more trust when both subjects had signed the petition than when one or both had not signed. The same behaviour is observed when we analyse high-cost political participation, namely, joining a street protest. This suggests that the experience of common participation in political collective action creates an identity that produces in-group favouritism. These results also suggest a reason why individuals choose to participate in political action despite private costs and a low probability of affecting the outcome: participation creates private benefits in subsequent interactions with fellow participants. |
| Keywords: | political identity, collective action, social preferences, laboratory experiment, petitions, street protests |
| JEL: | C91 D64 D79 D91 |
| Date: | 2021–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:col:000089:019932&r= |
| By: | Korpela, Ville; Lombardi, Michele; Saulle, Riccardo |
| Abstract: | We study rotation programs within the standard implementation framework under complete information. A rotation program is a myopic stable set whose states are arranged circularly, and agents can effectively move only between two consecutive states. We provide characterizing conditions for the implementation of efficient rules in rotation programs. Moreover, we show that the conditions fully characterize the class of implementable multi-valued and efficient rules. |
| Keywords: | Rotation Programs; Job Rotation; Assignment Problems; Implementation; rights structures; Stability. |
| JEL: | C7 D02 D04 D47 |
| Date: | 2021–12–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111126&r= |
| By: | Fredrik Carlsson; Claes Ek; Andreas Lange |
| Abstract: | We report experimental evidence on the voluntary provision of public goods under threshold uncertainty. By explicitly comparing two prominent technologies, summation and weakest link, we show that uncertainty is particularly detrimental to threshold attainment under weakest link, where low contributions by one subject cannot be compensated by others. In contrast, threshold uncertainty does not affect contributions under summation. We demonstrate non-binding pledges as one mechanism to improve chances of threshold attainment under both technologies, yet in particular under weakest link. |
| Keywords: | public goods, threshold uncertainty, weakest link, coordination, experiment |
| JEL: | C91 H41 Q54 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9457&r= |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, Paris School of Economics); Antoine Mandel (Centre d'Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, Paris School of Economics); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne, CNRS, Paris School of Economics) |
| Abstract: | We propose a model of the joint evolution of opinions and social relationships in a setting where social influence decays over time. The dynamics are based on bounded confidence: social connections between individuals with distant opinions are severed while new connections are formed between individuals with similar opinions. Our model naturally gives raise to strong diversity, i.e., the persistence of heterogeneous opinions in connected societies, a phenomenon that most existing models fail to capture. the intensity of social interactions is the key parameter that governs the dynamics. First, it determines the asymptotic distributionn of opinions. In particular, increasing the intensity of social interactions brings society closer to consensus. Second, it determines the risk of polariztion, which is shown to increase with the intensity of social interactions. Our results allow to frame the problem of the design of public debates in a formal setting. We hence characterize the optimal strategy for a social planner who controls the intensity of the public debate and thus faces a trade-off between the pursuit of social consensus and the risk of polarization. We also consider applications to political campaigning and show that both minority and majority candidates can have incentives to lead society towards polarization |
| Keywords: | opinion dynamics; network formation; network fragility; polarization; institution design; political campaign |
| JEL: | D85 C65 D83 |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:22001&r= |