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on Game Theory |
| By: | Berliant, Marcus |
| Abstract: | We examine the fine microstructure of commuting in a game-theoretic setting with a continuum of commuters. Commuters' home and work locations can be heterogeneous. A commuter transport network is exogenous. Traffic speed is determined by link capacity and by local congestion at a time and place along a link, where local congestion at a time and place is endogenous. The model can be reinterpreted to apply to congestion on the internet. We find sufficient conditions for existence of equilibrium, that multiple equilibria are ubiquitous, and that the welfare properties of morning and evening commute equilibria differ on a generalization of a directed tree. |
| Keywords: | Commuting; Internet traffic; Congestion externality; Efficient Nash equilibrium |
| JEL: | L86 R41 |
| Date: | 2023–12–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:119590&r=gth |
| By: | Pierre Bernhard (MACBES Team, INRIA, Université de Côte d'Azur, France); Marc Deschamps (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France) |
| Keywords: | Sticky price, Cournot oligopoly, Dynamic Game, Discrete time |
| JEL: | C61 C72 |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2024-01&r=gth |
| By: | Zhukovskaya, Lidia; Zhukovskiy, Vladislav; Mukhina, Julia |
| Abstract: | This article considers three new approaches to important problems of mathematical game theory and multicriteria choice.The first approach ensures payoff increase with simultaneous risk reduction in the Savage–Niehans sense in multicriteria choice problem and noncooperative games. The second approach allow us to stabilize coalitional structures in cooperative games without side payments under uncertainty. The third approach serves to integrate the selfish Nash equilibrium with the altruistic Berge equilibrium. Note that the investigations involve a special Germeier convolution of criteria and calculation of its saddle point in mixed strategies. |
| Keywords: | Savage–Niehans risk, minimax regret, uncertainties, multicriteria choice, Pareto consideration |
| JEL: | C00 |
| Date: | 2023–06–26 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:119394&r=gth |
| By: | Zhukovskiy, Vladislav; Zhukovskaya, Lidia; Mukhina, Yulia |
| Abstract: | The novelty of the approach presented below is that each person in a conflict (player) seeks not only to increase his payoff but also to reduce his risk, taking into account a possible realization of any uncertainty from a given admissible set. A new concept, the so-called strongly-guaranteed Nash equilibrium in payoffs and risks, is introduced and its existence in mixed strategies is proved under standard assumptions of the theory of noncooperative games, i.e., compactness and convexity of the sets of players’ strategies and continuity of the payoff functions. |
| Keywords: | Savage–Niehans risk, minimax regret, uncertainties, oncooperative game, optimal solution |
| JEL: | C00 C02 |
| Date: | 2023–06–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:119395&r=gth |
| By: | Harry Pei |
| Abstract: | I study repeated games with anonymous random matching where players can erase signals from their records. When players are sufficiently long-lived and have strictly dominant actions, they will play their dominant actions with probability close to one in all equilibria. When players' expected lifespans are intermediate, there exist purifiable equilibria with a positive level of cooperation in the submodular prisoner's dilemma but not in the supermodular prisoner's dilemma. Therefore, the maximal level of cooperation a community can sustain is not monotone with respect to players' expected lifespans and the complementarity in players' actions can undermine their abilities to sustain cooperation. |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2401.00839&r=gth |
| By: | Erhao Xie |
| Abstract: | This paper studies the testable implication of players’ collusive or cooperative behaviours in a binary choice game with complete information. In this paper, these behaviours are defined as players coordinating their actions to maximize the weighted sum of their payoffs. I show that this collusive model is observationally equivalent to an equilibrium model that imposes two restrictions. The first restriction is on each player’s strategic effect and the second one requires a particular equilibrium selection mechanism. Under the equilibrium condition, these joint restrictions are simple to test using tools in the literature on empirical games. This test, as suggested by the observational equivalence result, is the same as testing collusive and cooperative behaviours. I illustrate the implementation of this test by revisiting the entry game between Walmart and Kmart studied by Jia (2008). Under the equilibrium condition, Jia’s original estimates are consistent with the first restriction on the strategic effects, serving as a warning sign of potential collusion. This paper tests and rejects the second restriction on the equilibrium selection mechanism. Thus, the empirical evidence suggests that Walmart and Kmart did not collude on their entry decisions. |
| Keywords: | Econometric and statistical methods; Market structure and pricing |
| JEL: | C57 L13 |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:23-58&r=gth |
| By: | Anderson, E.; Holmberg, P. |
| Abstract: | We study multi-unit auctions where bidders have single-unit demand and asymmetric information. For symmetric equilibria, we identify circumstances where uniform-pricing is better for the auctioneer than pay-as-bid pricing, and where transparency improves the revenue of the auctioneer. An issue with the uniform-price auction is that seemingly collusive equilibria can exist. We show that such outcomes are less likely if the traded volume of the auctioneer is uncertain. But if bidders are asymmetric ex-ante, then both a price floor and a price cap are normally needed to get a unique equilibrium, which is well behaved. |
| Keywords: | Multi-unit auction, single-unit demand, uniform pricing, pay-as-bid, asymmetric information, publicity effect |
| JEL: | C72 D44 D82 |
| Date: | 2023–12–29 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2339&r=gth |
| By: | Reuter, Marco |
| Abstract: | I consider a seller selling a good to bidders with two-dimensional private information: their valuation for a good and their characteristic. While valuations are non-verifiable, characteristics are partially verifiable and convey information about the distribution of a bidder's valuation. I derive the revenue-maximizing mechanism and show that it can be implemented by introducing a communication stage before an auction. I show that granting bidders a right to remain anonymous, i.e., to refuse participation in the communication stage, leaves the optimal mechanism unchanged and provides no benefits for the bidders. |
| Keywords: | Mechanism Design, Auctions, Partially Verifiable Types, Communication |
| JEL: | D44 D82 D83 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:zewdip:280987&r=gth |
| By: | Dirk Bergemann (Yale University); Tibor Heumann (Pontificia Universidad Catolica de Chile); Stephen Morris (Massachusetts Institute of Technology) |
| Abstract: | We characterize the bidders' surplus maximizing information structure in an optimal auction for a single unit good and related extensions to multi-unit and multi-good problems. The bidders seeks to find a balance between participation (and the avoidance of exclusion) and efficiency. The information structure that maximizes the bidders surplus is given by a generalized Pareto distribution at the center of demand distribution, and displays complete information disclosure at either end of the Pareto distribution. |
| Date: | 2023–12–22 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2375&r=gth |
| By: | Joonkyung Yoo |
| Abstract: | Given a player is guaranteed the same payoff for each delivery path in a single-cube delivery network, the player's best response is to randomly divide all goods and deliver them to all other nodes, and the best response satisfies the Kuhn-Tucker condition. The state of the delivery network is randomly complete. If congestion costs are introduced to the player's maximization problem in a multi-cubic delivery network, the congestion paradox arises where all coordinates become congested as long as the previous assumptions about payoffs are maintained. |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2401.00940&r=gth |
| By: | Pietro Guarnieri; Lorenzo Spadoni |
| Abstract: | In this experimental study, we delve into the role of personal and social norms in an anti-coordination decision, such as the choice between staying home or going out in the El Farol Bar Game. Our design consists of two interconnected studies: in Study 1, we elicit either empirical or normative expectations before subjects make their decision in a one-shot El Farol Bar Game; in Study 2, subjects play two El Farol Bar games with different social-expectation primes. Our results reveal that the majority of subjects believe that staying home is the right thing to do and tend to act in accordance with their normative belief. Nevertheless, there is no prevailing consensus on what others believe is normatively right (normative expectations), and subjects do not base their decisions on these expectations. Conversely, a substantial majority of subjects expects that the predominant behavior is staying home (empirical expectations), and subjects tend to adhere to their empirical expectations. As far as social-expectation primes are concerned, they only lower subjects’ propensity to go out. This happens only when the prime conveys an empirical expectation to go out or a normative expectation to stay home. Furthermore, we observe a relatively low rate of change in the second El Farol Bar decision, and this does not hinge on the prime content. |
| Keywords: | Wealth; anti-coordination games; social expectations; normative beliefs |
| JEL: | C90 D83 D84 D91 |
| Date: | 2024–01–01 |
| URL: | http://d.repec.org/n?u=RePEc:pie:dsedps:2024/303&r=gth |
| By: | Liam Welsh; Sebastian Jaimungal |
| Abstract: | In response to the global climate crisis, governments worldwide are introducing legislation to reduce greenhouse gas (GHG) emissions to help mitigate environmental catastrophes. One method to encourage emission reductions is to incentivize carbon capturing and carbon reducing projects while simultaneously penalising excess GHG output. Firms that invest in carbon capturing projects or reduce their emissions can receive offset credits (OCs) in return. These OCs can be used for regulatory purposes to offset their excess emissions in a compliance period. OCs may also be traded between firms. Thus, firms have the choice between investing in projects to generate OCs or to trade OCs. In this work, we present a novel market framework and characterise the optimal behaviour of GHG OC market participants in both single-player and two-player settings. We analyse both a single-period and multi-period setting. As the market model does not elicit a closed form solution, we develop a numerical methodology to estimate players' optimal behaviours in accordance to the Nash equilibria. Our findings indicate the actions players take are dependent on the scale of their project opportunities as well as their fellow market participants. We demonstrate the importance of behaving optimally via simulations in order to offset emission penalties and the importance of investing in GHG reducing or capturing projects from a financial perspective. |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2401.01427&r=gth |
| By: | Zvonimir BaÅ¡ić (Adam Smith Business School, University of Glasgow, UK); Parampreet C. Bindra (University of Innsbruck); Daniela Glätzle-Rützler (University of Innsbruck, Austria); Angelo Romano (Leiden University, Netherlands); Matthias Sutter (Max Planck Institute for Research on Collective Goods, Bonn, University of Cologne, Germany, University of Innsbruck, Austria, IZA Bonn, Germany, and CESifo Munich); Claudia Zoller (Management Center Innsbruck) |
| Abstract: | We study the developmental roots of cooperation in 929 young children, aged 3 to 6. In a unified experimental framework, we examine pre-registered hypotheses about which of three fundamental pillars of human cooperation – direct reciprocity, indirect reciprocity, and third-party punishment – emerges earliest and is more effective as a means to increase cooperation in a repeated prisoner’s dilemma game. We find that already children aged 3 act in a conditionally cooperative way. Yet, direct and indirect reciprocity do not increase overall cooperation rates beyond a control condition. Compared to the latter, punishment more than doubles cooperation rates, making it the most effective mechanism to promote cooperation. We also find that children’s cognitive skills and parents’ socioeconomic background influence cooperation. We complement our experimental findings with a meta-analysis of studies on cooperation among adults and older children, confirming that punishment outperforms direct and indirect reciprocity. |
| Keywords: | Cooperation, reciprocity, third-party punishment, children, parents, prisoner’s dilemma game, experiment, meta-analysis |
| JEL: | C91 C93 D01 D91 H41 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2024_02&r=gth |
| By: | Tomas Sjostrom (Rutgers University; Kellogg School of Management, Northwestern University) |
| Abstract: | We study whether the Coase conjecture holds in a model of bargaining during conflict due to Powell and Fearon. Two players, A and B, contest a divisible resource. At any time during the conflict, they can make a binding agreement to share the resource. The conflict continues until they make an agreement or one side collapses. Player B privately knows w hether he is a strong or a weak type, with a greater probability of collapse if he is weak. The "lemons condition" says that player A would rather fight to the end than make a generous offer at the beginning of the conflict that both types of player B would accept. If this condition holds then the expected length of the conflict is bounded away from zero, even if negotiations are frictionless. Thus, the Coase conjecture does not hold. We study how the minimum length of conflict depends on the parameters, and the impact of third party intervention. |
| Keywords: | Conflict, Bargaining |
| JEL: | C7 |
| Date: | 2023–10–24 |
| URL: | http://d.repec.org/n?u=RePEc:rut:rutres:202301&r=gth |
| By: | Roland Bénabou (Princeton University, NBER, CEPR, IZA, BREAD, and briq); Armin Falk (University of Bonn); Luca Henkel (University of Chicago and University of CEMA, CESifo, JILAEE) |
| Abstract: | Choosing what is morally right can be based on the consequences (ends) resulting from the decision – the Consequentialist view – or on the conformity of the means involved with some overarching notion of duty – the Deontological view. Using a series of experiments, we investigate the overall prevalence and the consistency of consequentialist and deontological decision-making, when these two moral principles come into conflict. Our design includes a real-stakes version of the classical trolley dilemma, four novel games that induce ends-versus-means tradeoffs, and a rule-following task. These six main games are supplemented with six classical self-versus-other choice tasks, allowing us to relate consequential/deontological behavior to standard measures of prosociality. Across the six main games, we find a sizeable prevalence (20 to 44%) of non-consequentialist choices by subjects, but no evidence of stable individual preference types across situations. In particular, trolley behavior predicts no other ends-versus-means choices. Instead, which moral principle prevails appears to be context-dependent. In contrast, we find a substantial level of consistency across self-versus-other decisions, but individuals’ degree of prosociality is unrelated to how they choose in ends-versus-means tradeoffs. |
| Keywords: | morality, deontological, consequentialist, Kantian, ends-versus-means, trolley dilemma, prosocial, altruism, social preferences |
| JEL: | C91 D01 D64 |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:ajk:ajkdps:275&r=gth |
| By: | Luca Anderlini (Department of Economics, Georgetown University); Leonardo Felli (Faculty of Economics, University of Cambridge); Michele Piccione (London School of Economics) |
| Abstract: | How do mechanisms that enforce cooperation emerge in a society where none are available and agents are endowed with raw power, that allows a more powerful agent to expropriate a less powerful one? We study a model where expropriation is costly and agents can choose whether to engage in surplus-augmenting cooperation or engage in expropriation. While in bilateral relations, if cooperation is not overwhelmingly productive and expropriation is not too costly, the latter will prevent cooperation, when there are three or more agents, powerful ones can become enforcers of cooperation for agents ranked below them. In equilibrium they will expropriate smaller amounts from multiple weaker cooperating agents who in turn will not deviate for fear of being expropriated more heavily because of their larger expropriation proceeds. Surprisingly, the details of the power structure are irrelevant for the existence of equilibria with enforcement provided that enough agents are present and one is ranked above all others. These details are instead key to the existence of other highly non-cooperative equilibria that obtain in certain cases. |
| Keywords: | Jungle, Power Structures, Enforcement, Rule of Law |
| JEL: | C79 D00 D01 D31 K19 K40 K49 |
| Date: | 2023–12–13 |
| URL: | http://d.repec.org/n?u=RePEc:geo:guwopa:gueconwpa~23-23-06&r=gth |
| By: | D\'ora Gr\'eta Petr\'oczy; L\'aszl\'o Csat\'o |
| Abstract: | The Council of the European Union (EU) is one of the main decision-making bodies of the EU. Many decisions require a qualified majority: the support of 55% of the member states (currently 15) that represent at least 65% of the total population. We investigate how the power distribution, based on the Shapley-Shubik index, and the proportion of winning coalitions change if these criteria are modified within reasonable bounds. The influence of the two countries with about 4% of the total population each is found to be almost flat. The level of decisiveness decreases if the population criterion is above 68% or the states criterion is at least 17. The proportion of winning coalitions can be increased from 13.2% to 20.8% (30.1%) such that the maximal relative change in the Shapley--Shubik indices remains below 3.5% (5.5%). Our results are indispensable to evaluate any proposal for reforming the qualified majority voting system. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.16878&r=gth |