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on Game Theory |
| By: | Berliant, Marcus |
| Abstract: | Workers generally commute on a daily basis, so we model commuting as a repeated game. The folk theorem implies that for sufficiently large discount factors, the repeated commuting game has as a Nash equilibrium any feasible strategy that is uniformly better than the minimax strategy payoff for a commuter in the one shot game, repeated over the infinite horizon. This includes the efficient equilibria. An example where the efficient payoffs strictly dominate the one shot Nash equilibrium payoffs is provided. Our conclusions pose a challenge to congestion pricing in that equilibrium selection could be at least as effective in improving welfare. We examine evidence from St. Louis to determine what equilibrium strategies are actually played in the repeated commuting game. |
| Keywords: | Repeated game; Nash equilibrium; Commuting; Folk theorem |
| JEL: | R41 |
| Date: | 2023–02–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:116529&r=gth |
| By: | Mehmet S. Ismail |
| Abstract: | In this note, I introduce a new framework called $n$-person general-sum games with partial information, in which boundedly rational players have only limited information about the game -- including actions, outcomes, and other players. For example, playing an actual game of chess is a game of partial information. To analyze these games, I introduce a set of new concepts and metrics for measuring the performance of players, with a focus on the interplay between human- and machine-based decision-making. Specifically, I introduce (i) gaming-proofness, which is a property of a mechanism that players cannot game from a practical perspective, and (ii) the Net Game Points (NGP) mechanism, which measures the success of a player's performance in a game, taking into account both the outcome of the game and the ``mistakes'' made during the game. The NGP mechanism provides a practicable way to assess game outcomes and can potentially be applied to a wide range of games, from poker and football to AI systems, organizations, and companies. To illustrate the concept, I apply the NGP mechanism to select chess games played between some of the world's top players, including the world champion. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.13937&r=gth |
| By: | Besner, Manfred |
| Abstract: | The per capita Shapley support levels value extends the Shapley value to cooperative games with a level structure. This value prevents symmetrical groups of players of different sizes from being treated equally. We use efficiency, additivity, the null player property, and two new properties to give an axiomatic characterization. The first property, called joint productivity, is a fairness property within components and makes the difference to the Shapley levels value. If all players of two components are only jointly productive, they should receive the same payoff. Our second axiom, called neutral collusions, is a fairness axiom for players outside a component. Regardless of how players of a component organize their power, as long as the power of the coalitions that include all players of the component remains the same, the payoff to players outside the component does not change. |
| Keywords: | Cooperative game; Level structure; Per capita Shapley support levels value; Joint productivity; Neutral collusions |
| JEL: | C7 C71 |
| Date: | 2023–02–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:116457&r=gth |
| By: | Marco Reuter |
| Abstract: | I consider a seller selling a good to bidders with two-dimensional private information: their valuation for a good and their characteristic. While valuationsare 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: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_395&r=gth |
| By: | Robert Akerlof (University of Warwick); Hongyi Li (School of Economics, UNSW Business School); Jonathan Yeo (Nanyang Technological University) |
| Abstract: | This paper constructs a new game—the “rule-the-roost game”—where players compete repeatedly for power (“chickens”) and wealth (“eggs”) in the laboratory. We find that a vicious circle develops where the powerful accumulate more power and wealth over time, leading to substantial inequality. At the same time, the powerless take actions to oppose the powerful, which meaningfully reduces inequality. Gender differences are small in early rounds of the game but grow over time. The ratio of the female win rate to the male win rate declines by 1.3 percent each round, or 37.7 percent over the entire game. We argue that the growing difference is due to the vicious circle, which compounds the effects of small style-of-play differences. These findings suggest that gender imbalances may be particularly large in contexts such as firms where men and women interact repeatedly. |
| Keywords: | power, inequality, hierarchy, gender differences |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:swe:wpaper:2023-03&r=gth |
| By: | Brams, Steven; Ismail, Mehmet S.; Kilgour, Marc |
| Abstract: | Winning the coin toss at the end of a tied soccer game gives a team the right to choose whether to kick either first or second on all five rounds of penalty kicks, when each team is allowed one kick per round. There is considerable evidence that the right to make this choice, which is usually to kick first, gives a team a significant advantage. To make the outcome of a tied game fairer, we suggest a rule that handicaps the team that kicks first (A), requiring it to succeed on one more penalty kick than the team that kicks second (B). We call this the m - n rule and, more specifically, propose (m, n) = (5, 4): For A to win, it must successfully kick 5 goals before the end of the round in which B kicks its 4th; for B to win, it must succeed on 4 penalty kicks before A succeeds on 5. If both teams reach (5, 4) on the same round—when they both kick successfully at (4, 3)—then the game is decided by round-by-round “sudden death, ” whereby the winner is the first team to score in a subsequent round when the other team does not. We show that this rule is fair in tending to equalize the ability of each team to win a tied game in a penalty shootout. We also discuss a related rule that precludes the teams from reaching (5, 4) at the same time, obviating the need for sudden death and extra rounds. |
| Keywords: | Soccer, football, tie game, penalty shootouts, scoring rule |
| JEL: | C61 C72 |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:116352&r=gth |
| By: | Buccella, Domenico; Fanti, Luciano; Gori, Luca |
| Abstract: | In a three-country model in which export countries adopt environmental policies, this note analyses how abatement ("green") subsidy can become a potential strategic trade policy tool. When governments set the optimal policy tool considering their local environmental damages, a rich set of equilibria arise. In contrast to the standard result, it is shown that subsidising pollution abatement can 1) emerge as a Pareto-efficient equilibrium of the game; and 2) be the only feasible environmental policy when environmental awareness is low, irrespective of the technological efficiency. Therefore, "green" subsidies can lead to a win-win situation. |
| Keywords: | Abatement subsidy, Exports, International duopoly |
| JEL: | H23 F13 L13 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:glodps:1240&r=gth |
| By: | Amihai Glazer (Department of Economics University of California, Irvine); Hideki Konishi (Waseda Institute of Political Economy Waseda University) |
| Abstract: | Governmental officials often have far greater responsibilities and make far more consequential decisions than do CEOs of private firms. Nevertheless, governmental officials often earn far less and face low-powered incentives.We offer explanations for the differences, considering Nash bargaining with the head of a governmental agency or with the CEO of a for-profit firm. If regulations restrict the price a governmental agency can charge, or if at a governmental agency one official sets price and a different official negotiates pay, then the head of a governmental agency may earn less than the head of a for-profit firm. We also show that a governmental official paid less than a private CEO faces weaker incentives. That in turn can make costs, other than CEO pay, higher at a governmental agency. We also consider elections, with voters choosing an official to set the price of the good, and voters choosing an official to negotiate with the CEO over his pay. A governmental official will be paid less than a CEO at a private firm if the income distribution in the population is sufficiently unequal. |
| Keywords: | CEO pay, governmental officials, Nash bargaining, tax distortions, structureinduced equilibrium, low-powered incentives |
| JEL: | D23 H11 J31 J45 |
| URL: | http://d.repec.org/n?u=RePEc:wap:wpaper:2215&r=gth |
| By: | Chapkovski, Philipp; Zakharov, Alexei |
| Abstract: | Does the animosity toward a holder of an opposite political opinion or the behavior toward someone whose opinion on a divisive issue is unknown depends on whether that opinion was disclosed or withheld voluntarily? In order to study this question, we conducted a pre-registered study in Russia, measuring the pro-war dictators' behavior towards their partners with aligned or conflicting views on the war in Ukraine using give-or-take modification of Dictator Game. In the presence of a large polarisation gap (outgroup discrimination), we did not find that intentional vs. unintentional disclosure of the recipients' positions affected the transfers of the dictators; at the same time, dictators' beliefs about the share of war supporters among experiment participants and the donations made by other dictators were causally affected. Our study is the first one to consider this dimension of social interactions, and contributes to the quickly growing literature on political polarisation. |
| Keywords: | disclosure; transparency; polarization; dictator game; war in Ukraine; Russia |
| JEL: | C91 C92 D64 D74 D82 D83 |
| Date: | 2023–02–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:116305&r=gth |