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on Game Theory |
| By: | Olivier Bochet; Mathieu Faure; Yan Long; Yves Zenou (Division of Social Science) |
| Abstract: | We consider an aggregative game of competition in which agents have an imperfect knowledge about the set of agents they are in competition with. We model agent’s perceived competitors by a network in which each agent is assumed to only have information on the activities of their direct neighbors. In this framework, a natural equilibrium concept emerges, the peer-consistent equilibrium (PCE). In a PCE, each agent chooses an action level that maximizes her subjective perceived utility and the action levels of all individuals in the network must be consistent. We decompose the network into communities and completely characterize peer-consistent equilibria by identifying which sets of agents can be active in equilibrium. An agent is active if she either belongs to a strong community or if few agents are aware of her existence. We show that there is a unique stable PCE. We provide a behavioral foundation of eigenvector centrality, since, in any stable PCE, agents’ action levels are proportional to their eigenvector centrality in the network. We illustrate our results with two well-known models: Tullock contest function and Cournot competition. |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:nad:wpaper:20210069&r= |
| By: | Takaaki Abe (: School of Political Science and Economics, Waseda University, 1-6-1, Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan.); Satoshi Nakada (School of Management, Department of Business Economics, Tokyo University of Science, 1-11-2, Fujimi, Chiyoda-ku, Tokyo, 102-0071, Japan) |
| Abstract: | This paper considers the solution concepts of cooperative games that admit a potential function. We say that a solution admits a potential function if the solution is given as the gradient vector of the potential function at the player set. Hart and Mas-Collel (1989) show that the Shapley value is the only solution that is efficient and admits the potential function for games with variable player sets. In this paper, first, we argue that if we remove efficiency, various solutions admit a potential function. Second, we characterize the class of the solutions that admit a potential function and provide their general functional form. Third, we define a potential function for games with a fixed player set and associate a potential function with the axioms that the Shapley value obeys. Finally, we discuss how the efficiency requirement induces the uniqueness of the Shapley value through a potential function. |
| Keywords: | Cooperative games; Efficiency; Potential function; Shapley value |
| JEL: | C71 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:wap:wpaper:2114&r= |
| By: | Robert P. Gilles; Lina Mallozzi; Roberta Messalli |
| Abstract: | We study a class of non-cooperative aggregative games -- denoted as \emph{social purpose games} -- in which the payoffs depend separately on a player's own strategy (individual benefits) and on a function of the strategy profile which is common to all players (social benefits) weighted by an individual benefit parameter. This structure allows for an asymmetric assessment of the social benefit across players. We show that these games have a potential and we investigate its properties. We investigate the payoff structure and the uniqueness of Nash equilibria and social optima. Furthermore, following the literature on partial cooperation, we investigate the leadership of a single coalition of cooperators while the rest of players act as non-cooperative followers. In particular, we show that social purpose games admit the emergence of a stable coalition of cooperators for the subclass of \emph{strict} social purpose games. Due to the nature of the partial cooperative leadership equilibrium, stable coalitions of cooperators reflect a limited form of farsightedness in their formation. As a particular application, we study the tragedy of the commons game. We show that there emerges a single stable coalition of cooperators to curb the over-exploitation of the resource. |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2109.08471&r= |
| By: | Backhaus, Teresa; Breitmoser, Yves |
| Abstract: | Reanalyzing 12 experiments on the repeated prisoner's dilemma (PD), we robustly observe three distinct subject types: defectors, cautious cooperators and strong cooperators. The strategies used by these types are surprisingly stable across experiments and uncorrelated with treatment parameters, but their population shares are highly correlated with treatment parameters. As the discount factor increases, the shares of defectors decrease and the relative shares of strong cooperators increase. Structurally analyzing behavior, we next find that subjects have limited foresight and assign values to all states of the supergame, which relate to the original stage-game payoffs in a manner compatible with inequity aversion. This induces the structure of coordination games and approximately explains the strategies played using Schelling's focal points: after (c,c) subjects play according to the coordination game's cooperative equilibrium, after (d,d) they play according to its defective equilibrium, and after (c,d) or (d, c) they play according to its mixed equilibrium. |
| Keywords: | Repeated game,Behavior,Tit-for-tat,Mixed strategy,Memory,Belief-freeequilibrium,Laboratory experiment |
| JEL: | C72 C73 C92 D12 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbeoc:spii2021303&r= |
| By: | Demeze-Jouatsa, Ghislain-Herman (Center for Mathematical Economics, Bielefeld University); Pongou, Roland (Center for Mathematical Economics, Bielefeld University); Tondji, Jean-Baptiste (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | Frequent violations of fair principles in real-life settings raise the fundamental question of whether such principles can guarantee the existence of a self-enforcing equilibrium in a free economy. We show that elementary principles of distributive justice guarantee that a pure-strategy Nash equilibrium exists in a finite economy where agents freely (and non- cooperatively) choose their inputs and derive utility from their pay. Chief among these principles is that: 1) your pay should not depend on your name; and 2) a more productive agent should not earn less. When these principles are violated, an equilibrium may not exist. Moreover, we uncover an intuitive condition|technological monotonicity|that guarantees equilibrium uniqueness and efficiency. We generalize our findings to economies with social justice and inclusion, implemented in the form of progressive taxation and redistribution, and guaranteeing a basic income to unproductive agents. Our analysis uncovers a new class of strategic form games by incorporating normative principles into non-cooperative game theory. Our results rely on no particular assumptions, and our setup is entirely non- parametric. Illustrations of the theory include applications to exchange economies, surplus distribution in a firm, contagion and self-enforcing lockdown in a networked economy, and bias in the academic peer-review system. |
| Keywords: | Market justice, Social justice, Inclusion, Ethics, Discrimination, Self-enforcing contracts, Fairness in non-cooperative games, Pure strategy Nash equilibrium, Efficiency |
| Date: | 2021–09–16 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:653&r= |
| By: | Buccella, Domenico; Fanti, Luciano; Gori, Luca |
| Abstract: | This research contributes to the theory of cost-reducing R&D investments by offering a tractable three-stage non-cooperative Cournot duopoly game in which R&D-investing firms choose whether to disclose R&D-related information to the rival. Though in a noncooperative context firms have no incentive to unilaterally disclose information on their costreducing R&D activity to prevent the rival from freely appropriate it, this work shows that there is room for the government to design an optimal policy aimed at incentivising unilaterally each owner towards R&D disclosure. Under this welfare improving policy, sharing R&D-related information becomes a Pareto efficient Nash equilibrium strategy of selfish firms. These findings suggest that introducing public subsidies aimed at favouring R&D disclosure represents a win-win result, eliminating the so far established - and unpleasant for both firms and society - non-disclosing outcome. |
| Keywords: | Cost-reducing innovation,Nash equilibrium,Government,Social welfare |
| JEL: | D43 L13 O31 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:glodps:940&r= |
| By: | Fabien Gensbittel (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); Marcin Peski (University of Toronto); Jérôme Renault (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) |
| Abstract: | We define the distance between two information structures as the largest possible difference in value across all zero-sum games. We provide a tractable characterization of distance and use it to discuss the relation between the value of information in games versus single-agent problems, the value of additional information, informational substitutes, complements, or joint information. The convergence to a countable information structure under value-based distance is equivalent to the weak convergence of belief hierarchies, implying, among other things, that for zero-sum games, approximate knowledge is equivalent to common knowledge. At the same time, the space of information structures under the value-based distance is large: there exists a sequence of information structures where players acquire increasingly more information, and ε > 0 such that any two elements of the sequence have distance of at least ε. This result answers by the negative the second (and last unsolved) of the three problems posed by J.F. Mertens in his paper Repeated Games , ICM 1986. |
| Date: | 2021–09–16 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01869139&r= |
| By: | Takaaki Abe (School of Political Science and Economics, Waseda University, 1-6-1, Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan.); Satoshi Nakada (School of Management, Department of Business Economics, Tokyo University of Science, 1-11-2, Fujimi, Chiyoda-ku, Tokyo, 102-0071, Japan.) |
| Abstract: | Our objective is to analyze the relationship between the Shapley value and the core of cooperative games with transferable utility. We first characterize balanced games, namely, the set of games with a nonempty core, by means of geometric properties. We show that the set of balanced games generates a polyhedral cone and that a game is balanced if and only if it is a nonnegative linear combination of some simple games. Moreover, we show that the set of games whose Shapley value is in the core also yields a polyhedral cone and that a game obeys this property if and only if it is a nonnegative linear combination of some “easy” games. In addition, we also show that the number of games that correspond to the extreme rays of the polyhedron coincides with the number of minimal balanced collections. |
| Keywords: | Cooperative games; Shapley value; Core; Minkowski-Weyl’s Theorem |
| JEL: | C71 |
| Date: | 2021–06 |
| URL: | http://d.repec.org/n?u=RePEc:wap:wpaper:2112&r= |
| By: | Margherita Comola; Marcel Fafchamps |
| Abstract: | We conduct a laboratory experiment to study a decentralized market where goods are differentiated and evaluations are private. We implement different semi-structured bargaining protocols based on deferred acceptance, and we compare their performance to the benchmark scenario of a sealed-bid auction. We show that bargaining dramatically improves efficiency, mainly to the benefit of players rather than the silent auctioneer. A protocol of unconstrained simultaneous bargaining performs best, doubling the proportion of deals relative to the benchmark. This is because participants seek to reveal information through a gradual bidding-up strategy that favors bargaining environments. Aggregate efficiency nonetheless suffers from the fact that buyers bargain harder than sellers, and that some players over-bargain to appropriate a larger share of the unknown surplus. |
| JEL: | C78 C91 D47 D82 |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:29265&r= |
| By: | Dike Chukwudi Henry |
| Abstract: | We study properties of collective action problems bounded by minimal contributions as well as endowment and variable contributions are neighbourhood dependent. We relate nearness to non-interior agents and its implication for interior contribution. Here, we see the aspects of node distance to non-interior agents which have implications for interior agents. Endowments may be redistributed among agents. We highlight strict conditions for budget balanced transfers for which neighbourhood contributions and individual residual consumption’s are invariant. Agents may or may not be concerned about neighbourhood outcomes. We find that welfare is self correcting and neither cases are relevant to the overall welfare impact of neutral transfers. |
| Keywords: | Centrality; Contagion; Neutrality; Peer Effect |
| JEL: | C72 D85 H41 |
| Date: | 2021–06 |
| URL: | http://d.repec.org/n?u=RePEc:ukc:ukcedp:2107&r= |
| By: | Andrea Canidio; Heiko Karle |
| Abstract: | Two players with preferences distorted by the focusing effect (Koszegi and Szeidl, 2013) negotiate an agreement over several issues and one transfer. We show that, as long as their preferences are differentially distorted, an issue will be inefficiently left out of the agreement or inefficiently included in the agreement whenever the importance of the other issues on the table is sufficiently large. Anticipating this possibility, the negotiating parties may negotiate in stages, by first signing an incomplete agreement and later finalizing the outcome of the negotiation. Negotiating in stages increases the efficiency of the negotiation, despite the fact that the players’ preferences are distorted by the focusing effect also when negotiating the incomplete agreement. |
| Keywords: | salience, focusing effect, bargaining, negotiations, incomplete agreements |
| JEL: | C78 D03 D86 F51 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9297&r= |
| By: | Ata Atay; Eric Bahel; Tam\'as Solymosi |
| Abstract: | This paper studies matching markets in the presence of middlemen. In our framework, a buyer-seller pair may either trade directly or use the services of a middleman; and a middleman may serve multiple buyer-seller pairs. Direct trade between a buyer and a seller is costlier than a trade mediated by a middleman. For each such market, we examine an associated cooperative game with transferable utility. First, we show that an optimal matching for a matching market with middlemen can be obtained by considering the two-sided assignment market where each buyer-seller pair is allowed to use the mediation service of the middlemen free of charge and attain the maximum surplus. Second, we prove that the core of a matching market with middlemen is always non-empty. Third, we show the existence of a buyer-optimal core allocation and a seller-optimal core allocation. In general, the core does not exhibit a middleman-optimal matching. Finally, we establish the coincidence between the core and the set of competitive equilibrium payoff vectors. |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2109.05456&r= |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Tibor Heumann (Pontificia Universidad Católica de Chile); Stephen Morris (Dept. of Economics, MIT); Constantine Sorokin (Glasgow University and Higher School of Economics); Eyal Winter (The Hebrew University of Jerusalem) |
| Abstract: | In digital advertising, a publisher selling impressions faces a trade-off in deciding how precisely to match advertisers with viewers. A more precise match generates efficiency gains that the publisher can hope to exploit. A coarser match will generate a thicker market and thus more competition. The publisher can control the precision of the match by controlling the amount of information that advertisers have about viewers. We characterize the optimal trade-off when impressions are sold by auction. The publisher pools premium matches for advertisers (when there will be less competition on average) but gives advertisers full information about lower quality matches. |
| Keywords: | Second Price Auction, Conflation, Targeted Advertising, Impressions, Two-Sided Private Information, Bayesian Persuasion, Information Design |
| JEL: | D44 D47 D83 D84 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2300&r= |
| By: | Eitan Sapiro-Gheiler |
| Abstract: | I describe a Bayesian persuasion problem where Receiver has a private type representing a cutoff for choosing Sender's preferred action, and Sender has maxmin preferences over all Receiver type distributions with a known mean. Sender's utility from any distribution of posterior means is a function of its concavification; this result leads Sender to linearize the prior distribution by inducing a truncated uniform distribution of posterior means. When the prior belief about the state of the world is binary, Sender's unique optimal distribution is an upper-truncated uniform with an atom at 0. When the prior belief about the state of the world is continuous and unimodal, one optimal distribution for Sender is a double-truncated uniform with an atom at the end of the lower truncation. In both cases, the shape and support of the optimal distribution differ qualitatively from the corresponding solution when Sender holds a prior belief over Receiver types. |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2109.11536&r= |
| By: | Claudia Cerrone; Francesco Feri; Philip R. Neary |
| Abstract: | The outcome of a foregone alternative is not always learnt. We incorporate this observation into a model of regret, supposing that the ex-post information available depends on choice. We show that a more informative ex-post environment is never desirable for a regret averse individual. We then suppose that there are multiple regret averse individuals where the ex-post information available depends on own choice and the choices of others. This implies that what appears to be a series of isolated decision problems is in fact a behavioural game with multiple equilibria. We experimentally test the model and find support for our theory. |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2109.10968&r= |
| By: | Stephanie L. Chan (Xiamen University) |
| Abstract: | When there is strategic complementarity and all agents have access to public information, but only a subset of them has access to private information, strategic complementarity within the subset of privately-informed agents enhances the focal power of public information. This results to an expected social welfare function that is convex in the precision of both private and public information. The welfare gain from increasing the precision of the public information always exceeds the welfare loss from the underutilization of private information by a subset of agents. The results support the use of public information campaigns to change agent behavior regarding risky health behavior, public health crises and social injustices. The findings are robust to several extensions such as biased perceptions about public signals and costly acquisition of private information. |
| Keywords: | coordination, information asymmetry, private information, public information, strategic complementarity, welfare |
| JEL: | C70 D80 D82 D83 D84 |
| Date: | 2021–09–18 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002593&r= |
| By: | Olivier Bochet; Jacopo Magnani (Division of Social Science) |
| Abstract: | In vertically differentiated matching markets with private information, agents face an acceptance curse: being accepted as a partner conveys bad news. We experimentally investigate whether individuals anticipate the acceptance curse in such an environment. We test the effect of an exogenous change in reservation values which, by making some types more selective, induces significant changes in the posterior distribution of match qualities. Consistent with limited strategic sophistication, subjects do not respond to this manipulation. Through additional investigation and structural estimations, we suggest a mechanism explaining the lack of subjects’ response: out-of-equilibrium beliefs are quantitatively more important than limited conditional thinking. |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:nad:wpaper:20210071&r= |
| By: | John E. Stovall |
| Abstract: | A firm has a group of workers, each of whom has varying productivities over a set of tasks. After assigning workers to tasks, the firm must then decide how to distribute its output to the workers. We first consider three compensation rules and various fairness properties they may satisfy. We show that among efficient and symmetric rules: the Egalitarian rule is the only rule that is invariant to ``irrelevant'' changes in one worker's productivity; the Individual Contribution rule is the only rule that is invariant to the removal of workers and their assigned tasks; and the Shapley Value rule is the only rule that, for any two workers, equalizes the impact one worker has on the other worker's compensation. We introduce other rules and axioms, and relate each rule to each axiom. |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2109.04583&r= |
| By: | Olivier Bochet; Manshu Khanna; Simon Siegenthaler (Division of Social Science) |
| Abstract: | We design a laboratory experiment to study bargaining when parties need to agree on multiple issues. We find that bundling—the ability to make price offers on combinations of issues rather than separately—is critical for reaching agreement. We also find that giving bargainers access to more information about each other’s valuations and costs does not raise efficiency, because the boost in agreement rates in small-surplus negotiations is offset by increased risk-taking and conflicting fairness preferences in large-surplus negotiations. Finally, we show that successful negotiations are characterized by an alternating offer structure, which emerges endogenously. It involves offers that split the difference between the two most recent demands, and it displays a higher probability of agreement vis-a`-vis other formats of bargaining observed in our data. |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:nad:wpaper:20210070&r= |
| By: | Despoina Alempaki; Valeria Burdea; Daniel Read |
| Abstract: | In cases of conflict of interest, people can lie directly about payoff relevant private information, or they can evade the truth without lying directly. We analyse this situation theoretically and test the key predictions in an experimental sender-receiver setting. We find senders prefer to deceive through evasion rather than direct lying. This is because they do nοt want to deceive others, and they do nοt want to be seen as deceptive. The specific language of evasion does not matter. The results suggest deception should be tested in more naturalistic contexts with richer language. |
| JEL: | C91 D82 D83 D91 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9286&r= |
| By: | Brav, Alon; Dasgupta, Amil; Mathews, Richmond D. |
| Abstract: | Blockholder monitoring is central to corporate governance, but blockholders large enough to exercise significant unilateral influence are rare. Mechanisms that enable moderately-sized blockholders to exert collective influence are there-fore important. Existing theory suggests that engagement by moderately-sized blockholders is unlikely, especially when the blocks are held by delegated asset managers who have limited skin in the game. We present a model in which mul-tiple delegated blockholders engage target management in parallel, i.e., “wolf pack activism.” Delegation reduces skin in the game, which decreases incentives for engagement. However, it also induces competition over investor capital (i.e, competition for flow). We show that this increases engagement incentives and helps ameliorate the problem of insufficient engagement, though it can also fos-ter excess engagement. Under competition for flow the total amount of capital seeking skilled activist managers is relevant to engagement incentives, which helps to predict when and where wolf packs arise. Flow incentives are particularly valuable in incentivizing engagement by packs with smaller members |
| Keywords: | corporate governance; blockholder monitoring; institutional investors; reputation concerns; strategic complementarity; ES/S016686/1 |
| JEL: | G34 G23 |
| Date: | 2021–04–30 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:112118&r= |
| By: | Saglam, Ismail |
| Abstract: | Revelation principle implies that given any admissible social welfare function, the outcome of Baron and Myerson's (1982) (BM) optimal direct-revelation mechanism under incentive constraints cannot be dominated by any other mechanism in expected utilities. However, since the expected total surplus varies with a change in the social welfare function, Pareto improvements should be possible if the monopolist and consumers can agree, by means of side payments that reveal no additional information to the regulator, on the use of an alternative social welfare function which would generate a lower expected deadweight loss. We check the validity of this intuition by integrating the BM mechanism with an induced cooperative bargaining model where unilateral pre-donation by consumers or the producer is allowed. Under this new mechanism producer's pre-donation in the ex-ante stage always leads to ex-ante Pareto improvement while a certain amount of it completely eliminates the expected deadweight loss. Moreover, if optimally designed in the interim stage, the producer's pre-donation may also lead under some cost parameters to interim (and also (ex-post) Pareto improvement. Consumers, on the other hand, have no incentive to make a unilateral pre-donation, nor to reverse the optimal pre-donation of the monopolist. |
| Keywords: | Monopoly regulation; cooperative bargaining; pre-donation. |
| JEL: | C78 D42 L51 |
| Date: | 2021–09–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:109741&r= |
| By: | Jibang Wu; Ashwinkumar Badanidiyuru; Haifeng Xu |
| Abstract: | Classic mechanism design often assumes that a bidder's action is restricted to report a type or a signal, possibly untruthfully. In today's digital economy, bidders are holding increasing amount of private information about the auctioned items. And due to legal or ethical concerns, they would demand to reveal partial but truthful information, as opposed to report untrue signal or misinformation. To accommodate such bidder behaviors in auction design, we propose and study a novel mechanism design setup where each bidder holds two kinds of information: (1) private \emph{value type}, which can be misreported; (2) private \emph{information variable}, which the bidder may want to conceal or partially reveal, but importantly, \emph{not} to misreport. We show that in this new setup, it is still possible to design mechanisms that are both \emph{Incentive and Information Compatible} (IIC). We develop two different black-box transformations, which convert any mechanism $\mathcal{M}$ for classic bidders to a mechanism $\mathcal{M}'$ for strategically reticent bidders, based on either outcome of expectation or expectation of outcome, respectively. We identify properties of the original mechanism $\mathcal{M}$ under which the transformation leads to IIC mechanisms $\mathcal{M}'$. Interestingly, as corollaries of these results, we show that running VCG with expected bidder values maximizes welfare whereas the mechanism using expected outcome of Myerson's auction maximizes revenue. Finally, we study how regulation on the auctioneer's usage of information may lead to more robust mechanisms. |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2109.04888&r= |