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on Game Theory |
| By: | Florian Brandl; Felix Brandt |
| Abstract: | We give a robust characterization of Nash equilibrium by postulating coherent behavior across varying games: Nash equilibrium is the only solution concept that satisfies consequentialism, consistency, and rationality. As a consequence, every equilibrium refinement violates at least one of these properties. We moreover show that every solution concept that approximately satisfies consequentialism, consistency, and rationality returns approximate Nash equilibria. The latter approximation can be made arbitrarily good by increasing the approximation of the axioms. This result extends to various natural subclasses of games such as two-player zero-sum games, potential games, and graphical games. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.03079&r=gth |
| By: | Jacob K Goeree; Bernardo Garcia-Pola |
| Abstract: | $S$ equilibrium synthesizes a century of game-theoretic modeling. $S$-beliefs determine choices as in the refinement literature and level-$k$, without anchoring on Nash equilibrium or imposing ad hoc belief formation. $S$-choices allow for mistakes as in QRE, without imposing rational expectations. $S$ equilibrium is explicitly set-valued to avoid the common practice of selecting the best prediction from an implicitly defined set of unknown, and unaccounted for, size. $S$-equilibrium sets vary with a complexity parameter, offering a trade-off between accuracy and precision unlike in $M$ equilibrium. Simple "areametrics" determine the model's parameter and show that choice sets with a relative size of 5 percent capture 58 percent percent of the data. Goodness-of-fit tests applied to data from a broad array of experimental games confirm $S$ equilibrium's ability to predict behavior in and out of sample. In contrast, choice (belief) predictions of level-$k$ and QRE are rejected in most (all) games. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.06309&r=gth |
| By: | Pierpaolo Battigalli; Davide Bordoli |
| Abstract: | We analyze the infinite repetition with imperfect feedback of a simultaneous or sequential game, assuming that players are strategically sophisticated---but possibly impatient---expected-utility maximizers. Sophisticated strategic reasoning in the repeated game is combined with belief updating to provide a foundation for a refinement of self-confirming equilibrium. In particular, we model strategic sophistication as rationality and common strong belief in rationality. Then, we combine belief updating and sophisticated reasoning to provide sufficient conditions for a kind of learning--that is, the ability, in the limit, to exactly forecast the sequence of future observations--thus showing that impatient agents end up playing a sequence of self-confirming equilibria in strongly rationalizable conjectures of the one-period game. We also provide a converse of this result. Irrespective of whether individuals value the future, if they are able to learn then they will play in the limit a self-confirming equilibrium in strongly rationalizable conjectures of the continuation (infinitely repeated) game. Keywords: Self-confirming equilibrium; Common strong belief in rationality; Learning; Repeated games JEL classification: C72 ; C73 ; D83 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:702&r=gth |
| By: | Yiding Feng; Brendan Lucier; Aleksandrs Slivkins |
| Abstract: | We study a game played between advertisers in an online ad platform. The platform sells ad impressions by first-price auction and provides autobidding algorithms that optimize bids on each advertiser's behalf. Each advertiser strategically declares a budget constraint (and possibly a maximum bid) to their autobidder. The chosen constraints define an "inner" budget-pacing game for the autobidders, who compete to maximize the total value received subject to the constraints. Advertiser payoffs in the constraint-choosing "metagame" are determined by the equilibrium reached by the autobidders. Advertisers only specify budgets and linear values to their autobidders, but their true preferences can be more general: we assume only that they have weakly decreasing marginal value for clicks and weakly increasing marginal disutility for spending money. Our main result is that despite this gap between general preferences and simple autobidder constraints, the allocations at equilibrium are approximately efficient. Specifically, at any pure Nash equilibrium of the metagame, the resulting allocation obtains at least half of the liquid welfare of any allocation and this bound is tight. We also obtain a 4-approximation for any mixed Nash equilibrium, and this result extends also to Bayes-Nash equilibria. These results rely on the power to declare budgets: if advertisers can specify only a (linear) value per click but not a budget constraint, the approximation factor at equilibrium can be as bad as linear in the number of advertisers. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.07374&r=gth |
| By: | Igal Milchtaich (Bar-Ilan University) |
| Abstract: | Quantum advantage in Bayesian games, or games with incomplete information, refers to the larger set of correlated equilibrium outcomes that can be obtained by using quantum mechanisms rather than classical ones. Earlier examples of such advantage go under the title of quantum pseudo-telepathy. By using measurements of entangled particles, the players in the Mermin–Peres magic square game and similar games can obtain a common payoff that is higher than that afforded by any classical mechanism. However, these common-interest games are very special. In general games, where payoffs differ across players and player types, the implementation of specific correlated equilibrium outcomes may require limiting the information that different player types receive though the signals or messages they receive from a correlation device or mechanism. Because of the inherently destructive nature of measurements in quantum mechanics, it is well suited for this task. In a quantum correlated equilibrium, players choose what part of the information “encoded” in the quantum state to read, and choosing the part meant for their actual type is required to be incentive compatible. This requirement makes the choice of measurement analogous to the choice of report to the mediator in a communication equilibrium, and the measurement value is analogous to the massage sent back from the mediator. A choice of action follows. This paper systematically explores the advantage quantum mechanisms possess over comparable classical mechanisms in correlated and communication equilibria. It identifies the specific properties of quantum mechanisms responsible for these advantages. It then presents a classification of the equilibrium outcomes (both type-action distributions and equilibrium payoffs) in correlated and communication equilibria according to the kind of (classical or quantum) mechanism employed. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:biu:wpaper:2023-05&r=gth |
| By: | Xu Lang |
| Abstract: | We study games of chance (e.g., pokers, dices, horse races) in the form of agents' first-order posterior beliefs about game outcomes. We ask for any profile of agents' posterior beliefs, is there a game that can generate these beliefs? We completely characterize all feasible joint posterior beliefs from these games. The characterization enables us to find a new variant of Border's inequalities (Border, 1991), which we call a belief-based characterization of Border's inequalities. It also leads to a generalization of Aumann's Agreement Theorem. We show that the characterization results are powerful in bounding the correlation of agents' joint posterior beliefs. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.04070&r=gth |
| By: | Leonardo Becchetti; Vittorio Pelligra; Fiammetta Rossetti |
| Abstract: | A company that pursues illicit practices may crowd out competitors that behave legally eroding the public good of legality and integrity. Recently born institutional legality ratings tackle this problem. Redistributive policy actions aimed to tax “defectors” (i.e. buyers of unrated products) in favor of “co-operators” (i.e. buyers of “legality-rated” products) may further enforce legality, and fight corruption. We analyze the impact of the legality-rating frame by means of a randomized experiment. Our findings document that redistribution mechanisms, the legality frame and the conformity information design contribute to alleviate the prisoner’s dilemma and generate significant deviations from the Nash Equilibrium. |
| Keywords: | Corruption, Laboratory Experiment, Redistribution, Conformity |
| Date: | 2023–07–12 |
| URL: | http://d.repec.org/n?u=RePEc:ete:msiper:722267&r=gth |
| By: | Felix Kölle; Simone Quercia; Egon Tripodi |
| Abstract: | Social interactions predominantly take place under the shadow of the future. Previous literature explains cooperation in indefinitely repeated prisoner’s dilemma as predominantly driven by self-interested strategic considerations. This paper provides a causal test of the importance of social preferences for cooperation, varying the composition of interactions to be either homogeneous or heterogeneous in terms of these preferences. Through a series of pre-registered experiments (N = 1, 074), we show that groups of prosocial individuals achieve substantially higher levels of cooperation. The cooperation gap between prosocial and selfish groups persists even when the shadow of the future is increased to make cooperation attractive for the selfish and when common knowledge about group composition is removed. |
| Keywords: | cooperation, indefinitely repeated games, prisoner’s dilemma, social preferences, experiment |
| JEL: | C73 C91 C92 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10534&r=gth |
| By: | Bilancini, Ennio; Boncinelli, Leonardo; Nardi, Chiara; Pizziol, Veronica |
| Abstract: | We study how cooperation in one-shot Public Goods Games with large group sizes is affected by the presence of a slight chance of severe adverse events. We find that cooperation is substantial, notwithstanding a low marginal return of contributions. The cooperation level is comparable to what is found in similar settings for small-sized groups. Furthermore, we find no appreciable effect of the threat of severe adverse events, whether their realization is independent across individuals, perfectly positively or negatively correlated. We conclude that cooperation in the Public Goods Game is unlikely to be affected by rare adverse events, independently of how risk is correlated across individuals. |
| Date: | 2023–07–13 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:yrt63&r=gth |
| By: | Robert Balkin; Hector D. Ceniceros; Ruimeng Hu |
| Abstract: | In this paper, we propose a numerical methodology for finding the closed-loop Nash equilibrium of stochastic delay differential games through deep learning. These games are prevalent in finance and economics where multi-agent interaction and delayed effects are often desired features in a model, but are introduced at the expense of increased dimensionality of the problem. This increased dimensionality is especially significant as that arising from the number of players is coupled with the potential infinite dimensionality caused by the delay. Our approach involves parameterizing the controls of each player using distinct recurrent neural networks. These recurrent neural network-based controls are then trained using a modified version of Brown's fictitious play, incorporating deep learning techniques. To evaluate the effectiveness of our methodology, we test it on finance-related problems with known solutions. Furthermore, we also develop new problems and derive their analytical Nash equilibrium solutions, which serve as additional benchmarks for assessing the performance of our proposed deep learning approach. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.06450&r=gth |
| By: | Olivier Lindamulage de Silva (CRAN - Centre de Recherche en Automatique de Nancy - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique); Vineeth Varma (CRAN - Centre de Recherche en Automatique de Nancy - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique); Ming Cao (University of Groningen [Groningen]); Irinel-Constantin Morarescu (CRAN - Centre de Recherche en Automatique de Nancy - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique); Samson Lasaulce (CRAN - Centre de Recherche en Automatique de Nancy - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Stackelberg duopoly model in which two firms compete to maximize their market share is considered. The firms offer a service/product to customers that are spread over several geographical regions (e.g., countries, provinces, or states). Each region has its own characteristics (spreading and recovery rates) of each service propagation. We consider that the spreading rate can be controlled by each firm and is subject to some investment that the firm does in each region. One of the main objectives of this work is to characterize the advertising budget allocation strategy for each firm across regions to maximize its market share when competing. To achieve this goal we propose a Stackelberg game model that is relatively simple while capturing the main effects of the competition for market share. By characterizing the strong/weak Stackelberg equilibria of the game, we provide the associated budget allocation strategy. In this setting, it is established under which conditions the solution of the game is the so-called "winner takes all". Numerical results expand upon our theoretical findings and we provide the equilibrium characterization for an example. |
| Keywords: | Winner takes all, viral marketing, resource allocation, Stackelberg solution |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04150375&r=gth |
| By: | Martin Peitz; Susumu Sato |
| Abstract: | We propose a tractable model of asymmetric platform oligopoly in which users from two distinct groups are subject to within-group and cross-group network effects and decide which platform to join. We characterize the equilibrium when platforms manage user access by setting participation fees. We explore the effects of platform entry, change of incumbent platforms’ quality under free entry, and partial compatibility on market outcomes. We show how the analysis can be extended to partial user participation and zero fees for one of the user groups. |
| Keywords: | oligopoly theory, aggregative games, network effects, two-sided markets, two-sided single-homing, free entry, compatibility |
| JEL: | L13 L41 D43 |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_428v2&r=gth |
| By: | Rosina Rodríguez Olivera |
| Abstract: | I consider a model in which a monopolist data-seller offers information to privately informed data-buyers who play a game of incomplete information. I characterize the data-seller's optimal menu, which screens between two types of data-buyers. Data-buyers' preferences for information cannot generally be ordered across types. I show that the nature of data-buyers' preferences for information allows the data-seller to extract all surplus. In particular, the data-seller offers a perfectly informative experiment , which makes the data-buyer with the highest willingness to pay and a partially informative experiment, which makes the data-buyer with the highest willingness to pay for perfect information indifferent between both experiments. I also show that the features of the optimal menu are determined by the interaction between data-buyers' strategic incentives and the correlation of their private information. Namely, the data-seller offers two informative experiments even when data-buyers would choose the same action without supplemental information if data-buyers: i) have coordination incentives and their private information is negatively correlated or ii) have anti-coordination incentives and their private information is positively correlated. |
| Keywords: | Screening, Information, Strategic incentives |
| JEL: | D80 D82 |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_442&r=gth |
| By: | Sebastian Bervoets (Aix Marseille Univ, CNRS, AMSE, Marseille, France); Kohmei Makihara (Aix Marseille Univ, CNRS, AMSE, Marseille, France) |
| Abstract: | We consider public goods games played on a potentially non-symmetric network and provide comparative statics results on individual and aggregate contributions, as well as on the effect of transfers between players. We show that, contrary to the case of the complete and symmetric network, a positive shock on a player can have adverse consequences. First, it could actually decrease this player's contribution, unless the interaction matrix is a P-matrix. Second, a positive shock on a contributing player increases aggregate contributions, but a positive shock on a non-contributing player will decrease aggregate contributions, even if the player who benefited from the positive shock increases his own contribution. In each case we provide simple conditions to determine whether a positive shock will have positive or negative consequences on contributions, by looking at the unconstrained solution of an alternative, associated game. The sign of the coordinates of this solution determines the effect of a shock. With this in hand, we further show that the aggregate neutrality result of Andreoni [1990] regarding transfers between players generally does not hold on non-symmetric networks and provide conditions for it to hold. Finally, as an application of previous results, we consider introducing agents that follow Kantian moral principles and show that, depending on their position in the network, the presence of Kantian agents can, counter-intuitively, lead to a decrease in aggregate contributions. |
| Keywords: | public Goods, Network, comparative Statics, kantian players |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:aim:wpaimx:2317&r=gth |
| By: | Koukoumelis, Anastasios; Levati, Maria Vittoria Prof. (University of Verona); Nardi, Chiara |
| Abstract: | Many socially desirable actions are subject to risk and occur in situations where the others are not anonymous. Assessing whether lower subject-subject anonymity affects behavior when outcomes are risky is likely important but has not been studied in depth so far. Herein, we provide evidence on this issue. In a series of allocation tasks, all of them variations of the dictator game, we systematically vary the party who is exposed to risk and manipulate recipient anonymity by reducing the social and/or moral distance between the two parties. We propose a model that extends previous work by allowing not only for ex ante and ex post fairness but also for altruism. The model is consistent with observed behavior. In particular, a reduction in social and moral distance significantly increases the likelihood of equal split and more than equal split choices. |
| Date: | 2023–07–13 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:d8y4r&r=gth |
| By: | Shiri Alon; Sarah Auster; Gabi Gayer; Stefania Minardi |
| Abstract: | to adopt a new action. The receiver assesses the profitability of adopting the action by following a classical statistics approach: she forms an estimate via the similarity-weighted empirical frequencies of outcomes in past cases, sharing some attributes with the problem at hand. The sender has control over the characteristics of the sampled cases and discloses the outcomes of his study truthfully. We characterize the sender’s optimal sampling strategy as the outcome of a greedy algorithm. The sender provides more relevant data—consisting of observations sharing relatively more characteristics with the current problem—when the sampling capacity is low, when a large amount of initial public data is available, and when the estimated benefit of adoption according to this public data is low. Competition between senders curbs incentives for biasing the receiver’s estimate and leads to more balanced datasets. |
| Keywords: | Persuasion, case-based inference, similarity-weighted frequencies |
| JEL: | D81 D83 |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_443&r=gth |
| By: | Nicodemo De Vito (Department of Decision Sciences, Bocconi University) |
| Abstract: | Hierarchies of conditional beliefs (Battigalli and Siniscalchi 1999) play a central role for the epistemic analysis of solution concepts in sequential games. They are practically modelled by type structures, which allow the analyst to represent the players' hierarchies without specifying an infinite sequence of conditional beliefs. Here, we study type structures that satisfy a "richness" property, called completeness. This property is defined on the type structure alone, without explicit reference to hierarchies of beliefs or other type structures. We provide sufficient conditions under which a complete type structure represents all hierarchies of conditional beliefs. In particular, we present an extension of the main result in Friedenberg (2010) to type structures with conditional beliefs. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.05630&r=gth |
| By: | Tsuyoshi Toshimitsu (School of Economics, Kwansei Gakuin University) |
| Abstract: | Based on a horizontal product differentiation model associated with network externalities, we consider the impact of compatibility (interconnectivity) on incentives to innovate in a network goods industry in the cases of Cournot quantity and Bertrand price duopoly. We demonstrate that the effect of compatibility on incentives to innovate depends on network externalities and product substitutability. In particular, an increase in the degree of compatibility increases the incentives to innovate if the degree of network externalities is relatively large and if the degree of product differentiation is sufficiently large, irrespective of the mode of competition. Then, we then examine the same problem in a Hotelling-type unit-linear market and show that an increase in the degree of compatibility reduces the incentives to innovate. |
| Keywords: | innovation; network externality; compatibility; a fulfilled expectation; cost-reducing |
| JEL: | D43 L13 L15 O31 |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:kgu:wpaper:253&r=gth |
| By: | Herings, Jean-Jacques (Tilburg University, Center For Economic Research); Peeters, Ronald; Tenev, Anastas P. |
| Keywords: | social dilemma; cooperation; Reciprocity; Inertia |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:c547bbf9-1e82-44ce-94aa-fda166789375&r=gth |
| By: | Nicolas Piluso (CERTOP - Centre d'Etude et de Recherche Travail Organisation Pouvoir - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique, UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse) |
| Abstract: | The aim of this article is to model a negotiation between shareholders in high-technology-risk industries and local residents on the safety investments to be implemented. The methodology used is a Nash bargaining model, with a DE curve representing shareholders' dividend demands and an NS curve representing the safety demands of local residents' associations. The model is used to determine the level of safety investment required. One of the main results is that the estimation of a higher accident risk is accompanied by both a higher safety investment and a higher dividend payout. The most obvious implication of this result is that it is undoubtedly necessary to give greater weight to local residents in investment decision-making, in order to improve the well-being of all stakeholders. |
| Keywords: | Consultation, high-risk industries, safety investments, accident probability |
| Date: | 2023–05–30 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04154392&r=gth |