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on Game Theory |
| By: | Lucas Pahl |
| Abstract: | We present an index theory of equilibria for extensive form games. This requires developing an index theory for games where the strategy sets of players are general polytopes and their payoff functions are multiaffine in the product of these polytopes. Such polytopes arise from identifying (topologically) equivalent mixed strategies of a normal form game. |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2201.02098&r= |
| By: | Dong Hao; Qi Shi; Jinyan Su; Bo An |
| Abstract: | Revision game is a very new model formulating the situation where players can prepare and revise their actions in advance before a deadline when payoffs are realized. We identify the Limited Retaliation (LR) strategy for revision games which sustains a high level of mutual cooperation and is robust to players' occasional mistakes. The LR strategy stipulates that, (1) players first follow a recommended cooperative plan; (2) if anyone deviates from the plan, the LR player retaliates by using the defection action for a limited duration; (3) after the retaliation, the LR player returns to the cooperative plan. The LR strategy has two good features. First, it is vengeful, in the sense that it deters the opponent from non-cooperative action by threatening a retaliation. Second, it is forgiving, because it returns to cooperation after a proper retaliation. The vengeful feature makes it constitute a subgame perfect equilibrium, while the forgiving feature makes it tolerate occasional mistakes. These are in clear contrast to the existing strategies for revision games which all assume players are extremely grim and never forgive. Besides its contribution as a new robust and welfare-optimizing equilibrium strategy, our results about LR strategy can also be used to explain how easy cooperation can happen, and why forgiveness emerges in real-world multi-agent interactions. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.02271&r= |
| By: | Mallozzi, Lina; Vidal-Puga, Juan |
| Abstract: | In this paper, we study the generalization of (Nash) equilibrium and dominance solvability to interval fuzzy games in strategic form. We show that the more straightforward generalizations of these concepts do not inherit their most relevant results, either in terms of existence or refinement. To efficiently handle the fuzziness of the payoffs, we use the Hurwicz criterion and introduce new equilibrium concepts and dominance solutions that greatly overcome these drawbacks. |
| Keywords: | Dominance solvability; Fuzzy interval payoffs; Hurwicz criterion |
| JEL: | C72 |
| Date: | 2022–01–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111386&r= |
| By: | Harry Pei; Maren Vairo |
| Abstract: | A buyer and a seller bargain over the price of an object. The buyer's value is common knowledge and the seller has private information about his production cost. In the beginning of the game, each player proposes a price and becomes committed to it with small probability. We characterize the set of equilibria. We show that equilibria with inefficient delays exist if and only if the difference in cost between some pair of adjacent types is large enough and the probability of low-cost type seller is sufficiently high. When there are multiple equilibria, the buyer prefers the least efficient equilibrium and all types of the seller prefer the most efficient equilibrium. In an extension where the seller can decide whether to adopt a cost-saving technology before bargaining, we pin down the equilibrium adoption rate and provide conditions under which bargaining inefficiencies arise in all equilibria. |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2201.01827&r= |
| By: | Gonzalo Cisternas; Aaron Kolb |
| Abstract: | We study dynamic signaling when the informed party does not observe the signals generated by her actions. A forward-looking sender signals her type continuously over time to a myopic receiver who privately monitors her behavior; in turn, the receiver transmits his private inferences back through an imperfect public signal of his actions. Preferences are linear-quadratic and the information structure is Gaussian. We construct linear Markov equilibria using belief states up to the sender's second-order belief. Because of the private monitoring, this state is an explicit function of the sender's past play, leading to a novel separation effect through the second-order belief channel. Applications to models of organizations and reputation are examined. |
| Keywords: | signaling; private monitoring; continuous time |
| JEL: | C73 D82 D83 |
| Date: | 2021–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fednsr:93503&r= |
| By: | Christian Ewerhart |
| Abstract: | In a canonical model of military conflict, victory and defeat depend stochastically on the difference of resources deployed by the conflict parties. The present paper offers a com- prehensive analysis of that model. The unique Nash equilibrium reflects either (i) peace, (ii) submission, (iii) insurgency, or (iv) war. Intuitive predictions regarding possible transitions be- tween these types of equilibria are obtained. The analysis identifies advances in weaponry as an important driver of conflict and, less often so, of its resolution. The formal derivation exploits the variation-diminishing property of higher-order Pólya frequency functions. |
| Keywords: | Military conflict, difference-form contest, insurgency, Pólya frequency functions |
| JEL: | C02 C72 D74 |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:400&r= |
| By: | Andres Aradillas-Lopez (Institute for Fiscal Studies and University of Wisconsin); Adam Rosen (Institute for Fiscal Studies and Duke University) |
| Abstract: | We study inference in complete information games with discrete strategy spaces. Unlike binary games, we allow for rich strategy spaces and we only assume that they are ordinal in nature. We derive observable implications of equilibrium play under mild shape restrictions on payoff functions, and we characterize sharp identified sets for model parameters. We propose a novel inference method based on a test statistic that embeds conditional moment inequalities implied by equilibrium behavior. Our statistic has asymptotically pivotal properties that depend on the measure of contact sets, to which our statistic adapts automatically. In the case of two players and strategic substitutes we show that certain payoff parameters are point identified under mild conditions. We embed conventional point estimates for these parameters in our conditional moment inequality test statistic in order to perform inference on the remaining (partially identified) parameters. We apply our method to model the number of stores operated by Lowe’s and Home Depot in geographic markets and perform inference on several quantities of economic interest. |
| Date: | 2021–07–08 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:25/21&r= |
| By: | Nikos Tsakiris; Panos Hatzipanayotou; Michael S. Michael |
| Abstract: | In a model of two large asymmetric countries, we examine the effectiveness of the non-cooperative setting of tradable emission permits in reducing global pollution, under different rules of international taxation of capital earnings. Our key result is that, under certain conditions, the lowest Nash equilibrium level of global pollution is achieved when the policy-mix combines internationally, rather than nationally, tradable emission permits and either capital-tax exemptions or capital-tax credits. |
| Keywords: | Emission Permits; Cross-border Pollution; Capital Tax Competition; Capital Tax Rules |
| JEL: | F18 F21 H21 |
| Date: | 2022–01–14 |
| URL: | http://d.repec.org/n?u=RePEc:ucy:cypeua:01-2022&r= |
| By: | Rabia Nessah (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique, IESEG School of Management Lille); Tarik Tazdaït (CNRS - Centre National de la Recherche Scientifique, EHESS - École des hautes études en sciences sociales, ENPC - École des Ponts ParisTech); Mehrdad Vahabi (CEPN - Centre d'Economie de l'Université Paris Nord - LABEX ICCA - UP13 - Université Paris 13 - Université Sorbonne Nouvelle - Paris 3 - CNRS - Centre National de la Recherche Scientifique - UP - Université de Paris - Université Sorbonne Paris Nord - CNRS - Centre National de la Recherche Scientifique - Université Sorbonne Paris Nord) |
| Abstract: | In this paper, we are interested in exploring the history of game theory in France, and particularly the way it was received and was diffused in the fifties. It will be shown that France was the most fertile soil in the whole continental Europe for a multidisciplinary welcoming to game theory. Reviewing certain aspects of the intellectual trajectory of the mathematician Guilbaud, the ethnologist Lévi-Strauss and the psychanalyst Lacan, we show how each of them, in his own way, played a key role in advancing game theory: (1) Guilbaud for his constancy in disseminating game theory (and mathematics in general) (2) Lévi-Strauss for his original interpretation of game theory that had some impact on social sciences; and (3) Lacan for using the contributions of game theory. Lacan and Lévi-Strauss were particularly convincing since they were instructed on request about the principles of game theory by Guilbaud. |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03081226&r= |
| By: | Kasberger, Bernhard; Woodward, Kyle |
| 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. |
| Keywords: | Auctions; multi-unit auctions; loss minimization; non-Bayesian approaches |
| JEL: | D44 D81 |
| Date: | 2021–12–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111185&r= |
| By: | Simon Gaechter; Kyeongtae Lee; Martin Sefton; Till O. Weber |
| 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 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9449&r= |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Benjamin Brooks (Dept. of Economics, University of Chicago); Stephen Morris (Dept. of Economics, MIT) |
| Abstract: | We characterize the revenue-maximizing information structure in the second price auction. The seller faces a classic economic trade-o¤: providing more information improves the efficiency of the allocation but also creates higher information rents for bidders. The information disclosure policy that maximizes the revenue of the seller is to fully reveal low values (where competition will be high) but to pool high values (where competition will be low). The size of the pool is determined by a critical quantile that is independent of the distribution of values and only dependent on the number of bidders. We discuss how this policy provides a rationale for conflation in digital advertising. |
| JEL: | D44 D47 D83 D84 |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2318&r= |
| By: | Hiller, Victor (Universite Paris II Pantheon-Assas (LEMMA), Paris, France); Wu, Jiabin (Department of Economics, University of Oregon, Eugune, OR); Zhang, Hanzhe (Michigan State University, Department of Economics) |
| Abstract: | We demonstrate that marital preferences, the marriage market, and intergenerational transmission mechanisms must be jointly considered to gain a more complete picture of cultural evolution. We characterize cultural processes in settings with different combinations of (i) homophilic and heterophilic marital preferences, (ii) men-optimal or women-optimal stable matching scheme, and (iii) familial, societal, and rational forces of intergenerational transmission. First, with perfect vertical transmission in homogamies and oblique transmission in heterogamies, the presence of even a small fraction of heterophilic proposers leads to complete cultural homogeneity; cultural heterogeneity arises only when proposers are all homophilic. Notably, a stable matching scheme that is optimal for a gender in the short run can lead to suboptimal outcomes for them in the long run. Second, when transmission in heterogamies incorporates Darwinian consideration, persistent or temporary cycles between cultural homogeneity and heterogeneity may arise. Third, with imperfect vertical transmission in homogamies, heterophilic preferences and heterogamies play a significant role in the determination of cultural distribution; cultural substitutability is neither sufficient nor necessary for cultural heterogeneity. Finally, we discuss our model's implications for matriarchal and patriarchal societies, the evolution of gender roles as well as cultural assimilation and identity formation of minorities and immigrants. |
| Keywords: | cultural evolution; marital preferences; stable matching; intergenerational cultural transmission; imitative dynamics; evolutionary game theory |
| JEL: | C73 C78 D10 Z10 |
| Date: | 2021–12–31 |
| URL: | http://d.repec.org/n?u=RePEc:ris:msuecw:2022_001&r= |
| By: | Lijing Zhu (China University of Petroleum); Jingzhou Wang (China University of Petroleum); Arash Farnoosh (IFPEN - IFP Energies nouvelles - IFPEN - IFP Energies nouvelles, IFP School); Xunzhang Pan (China University of Petroleum) |
| Abstract: | To reduce traffic congestion and protect the environment, license plate control (LPC) policy has been implemented in Beijing since 2011. In 2019, 100,000 vehicle license plates were distributed, including 60,000 for electric vehicle (EV) and 40,000 for gasoline vehicle (GV). However, whether the current license plate allocation is optimal from a social welfare maximization perspective remains unclear. This paper proposes a two-level Stackelberg game which portrays the interaction between vehicle applicants and the government to quantify the optimal EV license plates under the LPC policy in Beijing. The equilibrium number of EV license plates derived from the Stackelberg model is 58,800, which could increase the social welfare by 0.38%. Sensitivity analysis is conducted to illustrate the impact of important influential factors — total license plate quota, vehicle rental fee, and energy price — on EV adoption. The LPC policy under COVID-19 is also studied through a scenario analysis. If the government additionally increases the total quota by 20,000, 24% could be allocated to GV and 76% to EV. One third reduction of the current vehicle rental fee could increase EV license plates by 10.5%. Interms of energy prices, when gasoline price is low, reducing electricity price could contribute to EV adoption significantly, while that effect tapers off as the gasoline price rises. |
| Keywords: | License plate quota,Stackelberg game theory,License plate control (LPC) policy,Electric vehicle |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03500766&r= |
| By: | Rapha\"el L\'evy; Marcin P\k{e}ski; Nicolas Vieille |
| Abstract: | We consider social learning in a changing world. Society can remain responsive to state changes only if agents regularly act upon fresh information, which limits the value of social learning. When the state is close to persistent, a consensus whereby most agents choose the same action typically emerges. The consensus action is not perfectly correlated with the state though, because the society exhibits inertia following state changes. Phases of inertia may be longer when signals are more precise, even if agents draw large samples of past actions, as actions then become too correlated within samples, thereby reducing informativeness and welfare. |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2201.02122&r= |
| By: | Frederico Finan; Demian Pouzo |
| Abstract: | This paper presents a framework for how to incorporate prior sources of information into the design of a sequential experiment. This information can come from many sources, including previous experiments, expert opinions, or the experimenter's own introspection. We formalize this problem using a multi-prior Bayesian approach that maps each source to a Bayesian model. These models are aggregated according to their associated posterior probabilities. We evaluate our framework according to three criteria: whether the experimenter learns the parameters of the payoff distributions, the probability that the experimenter chooses the wrong treatment when deciding to stop the experiment, and the average rewards. We show that our framework exhibits several nice finite sample properties, including robustness to any source that is not externally valid. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.09170&r= |
| By: | Andrea Galeotti; Benjamin Golub; Sanjeev Goyal; Eduard Talam\`as; Omer Tamuz |
| Abstract: | Suppliers of differentiated goods make simultaneous pricing decisions, which are strategically linked due to consumer preferences and the structure of production. Because of market power, the equilibrium is inefficient. We study how a policymaker should target a budget-balanced tax-and-subsidy policy to increase welfare. A key tool is a certain basis for the goods space, determined by the network of interactions among suppliers. It consists of eigenbundles -- orthogonal in the sense that a tax on any eigenbundle passes through only to its own price -- with pass-through coefficients determined by associated eigenvalues. Our basis permits a simple characterization of optimal interventions. For example, a planner maximizing consumer welfare should tax eigenbundles with low pass-through and subsidize ones with high pass-through. We interpret these results in terms of the network structure of the market. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.08153&r= |