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on Game Theory |
| By: | David Lowing (Kyushu University); Makoto Yokoo (Kyushu University) |
| Abstract: | A Sharing value for transferable utility games distributes the Harsanyi dividend of each coalition among the players in the coalition's support. Such distribution is done according to a certain sharing system that determines the Sharing value. In this paper, we extend Sharing values to multi-choice games. Multi-choice games are a generalization of transferable utility games in which players have several activity levels. Unlike in transferable utility games, there is no straightforward way to interpret the support of a coalition in a multi-choice game. This makes it more tedious to distribute the Harsanyi dividend of a multi-choice coalition. We consider three possible interpretations of the support of a multi-choice coalition. Based on these interpretations, we derive three families of Sharing values for multi-choice games. To conduct this study, we discuss novel and classical axioms for multi-choice games. This allows us to provide an axiomatic foundation for each of these families of values. |
| Keywords: | Multi-choice games, Sharing values, Harsanyi set |
| Date: | 2023–03–08 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-04018735&r=gth |
| By: | Giuseppe Attanasi (Université Côte d'Azur, France; GREDEG CNRS); Michela Chessa (Université Côte d'Azur, France; GREDEG CNRS); Sara Gil Gallen (Università degli studi di Bari "Aldo Moro", Italy); Elena Manzoni (University of Bergamo) |
| Abstract: | We investigate theoretically and experimentally the performance of a bargaining-overstrategies protocol with confirmed proposals, with either symmetric (i.e., alternating among the two players) or asymmetric power of confirmation (i.e., assigned to one of the two players alone). We apply it both to a Bertrand duopoly market, in which competition is on prices, and to a Cournot duopoly market, in which players compete on the amount of output they produce. We characterize the set of subgame perfect equilibrium outcomes of the bargaining game with confirmed proposals for each of the four combinations of confirmation power and market game, and formulate theory-driven hypotheses based on these different characterizations. Our experimental results show that bargaining over strategies of price- or quantity-setting (i) acts as a communication device in competitive environments, (ii) increases the level of collusion, and (iii) reduces the bargaining length. In particular, we report experimental evidence of overall better performance of a Bertrand duopoly market in reaching an equitable, welfare-maximizing, and Pareto-efficient agreement. However, competing in price rather than in quantity setting reduces the bargaining length only under asymmetric power of confirmation, while under symmetric power price-setting only has a second-order effect on reducing the bargaining length. We complement the data analysis with a qualitative analysis of the sequence of players' declared strategies as communication devices. |
| Keywords: | Bargaining, Tacit collusion, Experiments, Bertrand duopoly, Cournot duopoly |
| JEL: | C72 C91 |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2022-18&r=gth |
| By: | Claus-Jochen Haake (Paderborn University); Thomas Streck (Paderborn University) |
| Abstract: | We study the consequences of modeling asymmetric bargaining power in two- person bargaining problems. Comparing the application of an asymmetric version of a bargaining solution to an upfront modification of the disagreement point, the resulting distortion crucially depends on the bargaining solution concept. While for the Kalai-Smorodinsky solution a weak player benefits from modifying the disagreement point, the situation is reversed for the Nash bargaining solution. There, weaker players are better o in the asymmetric bargaining solution. When comparing the application of the asymmetric versions of the Nash and the Kalai-Smorodinsky solutions, we demonstrate that there is an upper bound for the weight of a player, so that she is better o with the Nash bargaining solution. This threshold is ultimately determined by the relative utilitarian bargaining solution. From a mechanism design perspective, our results provide valuable information for a social planner, when implementing a bargaining solution for unequally powerful players. |
| Keywords: | Asymmetric bargaining power, Nash bargaining solution, Kalai-Smorodinsky bargaining solution |
| JEL: | C78 D63 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:ciepap:155&r=gth |
| By: | Xi Chen; Binghui Peng |
| Abstract: | We study the complexity of finding an approximate (pure) Bayesian Nash equilibrium in a first-price auction with common priors when the tie-breaking rule is part of the input. We show that the problem is PPAD-complete even when the tie-breaking rule is trilateral (i.e., it specifies item allocations when no more than three bidders are in tie, and adopts the uniform tie-breaking rule otherwise). This is the first hardness result for equilibrium computation in first-price auctions with common priors. On the positive side, we give a PTAS for the problem under the uniform tie-breaking rule. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.16388&r=gth |
| By: | Julio Huato |
| Abstract: | This paper models a two-agent economy with production and appropriation as a noncooperative dynamic game, and determines its closed-form Markovian Nash equilibrium. The analysis highlights the para-metric conditions that tip the economy from a nonaggressive or "co-operative" equilibrium to outright distributional conflict. The model includes parameters that capture the role of appropriation technology and destructiveness. The full dynamic implications of the game are yet to be explored, but the model offers a promising general framework for thinking about different technological and economic conditions as more or less conducive to cooperation or distributional conflict. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.01855&r=gth |
| By: | Justin Diamond; Ben Garcia |
| Abstract: | "Egyptian Ratscrew" (ERS) is a modern American card game enjoyed by millions of players worldwide. A game of ERS is won by collecting all of the cards in the deck. Typically this game is won by the player with the fastest reflexes, since the most common strategy for collecting cards is being the first to slap the pile in the center whenever legal combinations of cards are placed down. Most players assume that the dominant strategy is to develop a faster reaction time than your opponents, and no academic inquiry has been levied against this assumption. This thesis investigates the hypothesis that a "risk slapping" strategist who relies on practical economic decision making will win an overwhelming majority of games against players who rely on quick reflexes alone. It is theorized that this can be done by exploiting the "burn rule, " a penalty that is too low-cost to effectively dissuade players from slapping illegally when it benefits them. Using the Ruby programming language, we construct an Egyptian Ratscrew simulator from scratch. Our model allows us to simulate the behavior of 8 strategically unique players within easily adjustable parameters including simulation type, player count, and burn amount. We simulate 100k iterations of 67 different ERS games, totaling 6.7 million games of ERS, and use win percentage data in order to determine which strategies are dominant under each set of parameters. We then confirm our hypothesis that risk slapping is a dominant strategy, discover that there is no strictly dominant approach to risk slapping, and elucidate a deeper understanding of different ERS mechanics such as the burn rule. Finally, we assess the implications of our findings and suggest potential improvements to the rules of the game. We also touch on the real-world applications of our research and make recommendations for the future of Egyptian Ratscrew modeling. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.01007&r=gth |
| By: | O. A. Malafeyev; N. D. Redinskikh; V. F. Bogachev |
| Abstract: | In this paper, the interaction of geopolitical actors in the production and sale of military equipment is studied. In section 2 the production of military equipment is considered as the two person zero-sum game. In such game, the strategies of the players are defined by the information state of the actors. The optimal strategy of geopolitical actors is found. In section 3, the conflict process is considered, the optimal strategy is determined for each geopolitical actor. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.07568&r=gth |
| By: | Matthew Kovach; Gerelt Tserenjigmid |
| Abstract: | We propose a generalization of Quantal Response Equilibrium (QRE) built on a simple premise: some actions are more focal than others. In our model, which we call the Focal Quantal Response Equilibrium (Focal QRE), each player plays a stochastic version of Nash equilibrium as in the QRE, but some strategies are focal and thus are chosen relatively more frequently than other strategies after accounting for expected utilities. The Focal QRE is able to systemically account for various forms of bounded rationality of players, especially regret-aversion, salience, or limited consideration. The Focal QRE is also useful to explain observed heterogeneity of bounded rationality of players across different games. We show that regret-based focal sets perform relatively well at predicting strategies that are chosen more frequently relative to their expected utilities. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.00438&r=gth |
| By: | Meng-Jhang Fong; Po-Hsuan Lin; Thomas R. Palfrey |
| Abstract: | In this short note, we compare the cursed sequential equilibrium (CSE) by Fong et al. (2023) and the sequential cursed equilibrium (SCE) by Cohen and Li (2023). We identify eight main differences between CSE and SCE with respect to the following features: (1) the family of applicable games, (2) the number of free parameters, (3) the belief updating process, (4) the treatment of public histories, (5) effects in games of complete information, (6) violations of subgame perfection and sequential rationality, (7) re-labeling of actions, and (8) effects in one-stage simultaneous-move games. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.05515&r=gth |
| By: | Masaaki Fujii; Masashi Sekine |
| Abstract: | In this paper, we study a problem of equilibrium price formation among many investors with exponential utility. The investors are heterogeneous in their initial wealth, risk-averseness parameter, as well as stochastic liability at the terminal time. We characterize the equilibrium risk-premium process of the risky stocks in terms of the solution to a novel mean-field backward stochastic differential equation (BSDE), whose driver has quadratic growth both in the stochastic integrands and in their conditional expectations. We prove the existence of a solution to the mean-field BSDE under several conditions and show that the resultant risk-premium process actually clears the market in the large population limit. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.07108&r=gth |
| By: | Jos Jansen (Department of Economics and Business Economics, Aarhus University) |
| Abstract: | I study the incentives of Cournot duopolists to share their technologies with their competitor in markets where intellectual property rights are absent and imitation is costless. The trade-off between a signaling effect and an expropriation effect determines the technology-sharing incentives. In equilibrium, there tends to be at most one firm that shares technologies. For similar technology distributions, there exists an equilibrium in which nobody shares. If the technology distributions are skewed towards efficient technologies, then there may exist equilibria in which one firm shares all technologies, only the best technologies, or only intermediate technologies. Further, I consider several extensions. |
| Keywords: | Cournot duopoly, strategic disclosure, indivisibility, innovation, trade secret, open source, skewed distribution |
| JEL: | D82 L13 L17 O32 O34 |
| Date: | 2023–05–03 |
| URL: | http://d.repec.org/n?u=RePEc:aah:aarhec:2023-04&r=gth |
| By: | Ralph Winkler |
| Abstract: | Many poor countries are ill-adapted to the current leave alone a changing future climate, because they lack the necessary financial means to invest in efficient and cost-effective safeguarding measures. International endeavours to fund institutions, such as the Green Climate Fund, to provide financial assistance in this respect have not been as successful has hoped for. In this paper, I set up a simple two-player two-stage model, in which a rich country (North) can invest into adaptation measures in a poor country (South). I show that a necessary condition for North to invest into adaptation investments in South is that this results in decreasing equilibrium emissions of South. I find that this can only happen if the funded adaptation measures also have a flavor of mitigation, i.e., apart from safeguarding South from climate damages they have to reduce South’s marginal abatement costs. My results have important policy implications for the selection of adaptation and mitigation projects by international adaptation funding organizations, such as the Green Climate Fund. |
| Keywords: | climate change, adaptation versus mitigation, cross-country adaptation investments, non-cooperative climate policy, strategic complementarity |
| JEL: | C72 D62 H41 Q54 Q58 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10371&r=gth |
| By: | Caliendo, Marco (University of Potsdam); Cobb-Clark, Deborah A. (University of Sydney); Silva Goncalves, Juliana (University of Sydney); Uhlendorff, Arne (CREST) |
| Abstract: | We conduct a laboratory experiment to study how locus of control operates through people's preferences and beliefs to influence their decisions. Using the principal-agent setting of the delegation game, we test four key channels that conceptually link locus of control to decision- making: (i) preference for agency; (ii) optimism and (iii) confidence regarding the return to effort; and (iv) illusion of control. Knowing the return and cost of stated effort, principals either retain or delegate the right to make an investment decision that generates payoffs for themselves and their agents. Extending the game to the context in which the return to stated effort is unknown allows us to explicitly study the relationship between locus of control and beliefs about the return to effort. We find that internal locus of control is linked to the preference for agency, an effect that is driven by women. We find no evidence that locus of control influences optimism and confidence about the return to stated effort, or that it operates through an illusion of control. |
| Keywords: | locus of control, preference for agency, decision-making, beliefs, optimism, confidence, illusion of control |
| JEL: | D83 D87 D91 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp16061&r=gth |
| By: | Aïd, René (Center for Mathematical Economics, Bielefeld University); Basei, Matteo (Center for Mathematical Economics, Bielefeld University); Ferrari, Giorgio (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We consider a mean-field model of firms competing à la Cournot on a commodity market, where the commodity price is given in terms of a power inverse demand function of the industry-aggregate production. Investment is irreversible and production capacity depreciates at a constant rate. Production is subject to Gaussian productivity shocks, while large non-anticipated macroeconomic events driven by a two-state continuous-time Markov chain can change the volatility of the shocks, as well as the price function. Firms wish to maximize expected discounted revenues of production, net of investment and operational costs. Investment decisions are based on the long-run stationary price of the commodity. We prove existence, uniqueness and characterization of the stationary mean-field equilibrium of the model. The equilibrium investment strategy is of barrier-type and it is triggered by a couple of endogenously determined investment thresholds, one per state of the economy. We provide a quasi-closed form expression of the stationary density of the state and we show that our model can produce Pareto distribution of firms' size. This is a feature that is consistent both with observations at the aggregate level of industries and at the level of a particular industry. We establish a relation between economic instability and market concentration and we show how macroeconomic instability can harm firms' profitability more than productivity fluctuations. |
| Keywords: | mean-field stationary equilibrium, irreversible investment, regime-switching, market concentration, value of economic stability |
| Date: | 2023–05–02 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:679&r=gth |
| By: | Dirk Bergemann; Alessandro Bonatti; Nicholas Wu |
| Abstract: | We develop an auction model for digital advertising. A monopoly platform has access to data on the value of the match between advertisers and consumers. The platform support bidding with additional information and increase the feasible surplus for on-platform matches. Advertisers jointly determine their pricing strategy both on and off the platform, as well as their bidding for digital advertising on the platform. We compare a data-augmented second-price auction and a managed campaign mechanism. In the data-augmented auction, the bids by the advertisers are informed by the data of the platform regarding the value of the match. This results in a socially efficient allocation on the platform, but the advertisers increase their product prices off the platform to be more competitive on the platform. In consequence, the allocation off the platform is inefficient due to excessively high product prices. The managed campaign mechanism allows advertisers to submit budgets that are then transformed into matches and prices through an autobidding algorithm. Compared to the data-augmented second-price auction, the optimal managed campaign mechanism increases the revenue of the digital platform. The product prices off the platform increase and the consumer surplus decreases. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.08432&r=gth |
| By: | Domenico Buccella; Luciano Fanti; Luca Gori |
| Abstract: | In a Cournot duopoly with indirect taxes evasion, this paper counter-intuitively shows that, in the presence of unions, a higher indirect taxation may increase profits because taxes reduce wage claims. This result is likely to occur if the market size is adequately large and the detection probability is not too high. Moreover, unionisation 1) leaves unaltered the absolute while reduces the relative tax evasion; and 2) increases tax revenue. As consumer and social welfare are unaffected by taxation, the policy implication is that higher taxes (which are always revenue-enhancing) ultimately lead to a redistribution from wages to profits. |
| Keywords: | Tax Evasion, Sales Tax, Cournot duopoly, Unions |
| JEL: | H20 H25 H26 J5 |
| Date: | 2023–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:pie:dsedps:2023/293&r=gth |
| By: | Xiaoliang Li; Kongyan Chen; Wei Niu; Bo Huang |
| Abstract: | Since Kopel's duopoly model was proposed about three decades ago, there are almost no analytical results on the equilibria and their stability in the asymmetric case. The first objective of our study is to fill this gap. This paper analyzes the asymmetric duopoly model of Kopel analytically by using several tools based on symbolic computations. We discuss the possibility of the existence of multiple positive equilibria and establish necessary and sufficient conditions for a given number of positive equilibria to exist. The possible positions of the equilibria in Kopel's model are also explored. Furthermore, if the duopolists adopt the best response reactions or homogeneous adaptive expectations, we establish rigorous conditions for the existence of distinct numbers of positive equilibria for the first time. The occurrence of chaos in Kopel's model seems to be supported by observations through numerical simulations, which, however, is challenging to prove rigorously. The second objective is to prove the existence of snapback repellers in Kopel's map, which implies the existence of chaos in the sense of Li-Yorke according to Marotto's theorem. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.02136&r=gth |
| By: | Dirk Bergemann; Alessandro Bonatti |
| Abstract: | We analyze digital markets where a monopolist platform uses data to match multiproduct sellers with heterogeneous consumers who can purchase both on and off the platform. The platform sells targeted ads to sellers that recommend their products to consumers and reveals information to consumers about their values. The revenue-optimal mechanism is a managed advertising campaign that matches products and preferences efficiently. In equilibrium, sellers offer higher qualities at lower unit prices on than off the platform. Privacy-respecting data-governance rules such as organic search results or federated learning can lead to welfare gains for consumers. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.07653&r=gth |