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on Game Theory |
| By: | van Beek, Andries (Tilburg University, Center For Economic Research); Borm, Peter (Tilburg University, Center For Economic Research) |
| Keywords: | entangled equilibrium; Nash equilibrium refinement; bimatrix game |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:tiu:tiucen:834facb8-8e33-4046-a452-715719ef244e |
| By: | Florian Herold (University of Bamberg, Germany); Christoph Kuzmics (University of Graz, Austria) |
| Abstract: | In a finite two player game consider the matrix of one player's payoff difference between any two consecutive pure strategies. Define the half space induced by a column vector of this matrix as the set of vectors that form an obtuse angle with this column vector. We use Farkas' lemma to show that this player can be made indifferent between all pure strategies if and only if the union of all these half spaces covers the whole vector space. This result leads to a necessary (and almost sufficient) condition for a game to have a completely mixed Nash equilibrium. We demonstrate its usefulness by providing the class of all symmetric two player three strategy games that have a unique and completely mixed symmetric Nash equilibrium. |
| Keywords: | completely mixed strategies, mixed Nash equilibria, Farkas' lemma. |
| JEL: | C72 |
| Date: | 2024–03 |
| URL: | https://d.repec.org/n?u=RePEc:grz:wpaper:2024-08 |
| By: | Lu Yu |
| Abstract: | To generalize complementarities for games, we introduce some conditions weaker than quasisupermodularity and the single crossing property. We prove that the Nash equilibria of a game satisfying these conditions form a nonempty complete lattice. This is a purely order-theoretic generalization of Zhou's theorem. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.00636 |
| By: | Lu Yu |
| Abstract: | We prove three results on the existence and structure of Nash equilibria for quasisupermodular games. A theorem is purely order-theoretic, and the other two involve topological hypotheses. Our topological results genralize Zhou's theorem (for supermodular games) and Calciano's theorem. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.13783 |
| By: | Michael Finus (University of Graz, Austria); Francesco Furini (University of Hamburg, Germany); Anna Viktoria Rohrer (University of Graz, Austria) |
| Abstract: | A commonly reported result in the literature on international environmental agreements (IEAs) is that if coalition members act as Stackelberg leaders (Stackelberg scenario) this leads to larger stable coalitions than if signatories act simultaneously with non-signatories. (Nash-Cournot scenario). This result has been taken for granted, a kind of Folk-theorem, even though it has been proven at best for specific payoff functions, and very often the conclusion is only based on simulations. We prove the Stackelberg vs. Nash-Cournot Folk-theorem based on a generic payoff function for a public good provision game. |
| Keywords: | International environmental agreements, Stability, Stackelberg vs. Nash-Cournot Folk-theorem. |
| JEL: | C72 D62 H41 |
| Date: | 2024–01 |
| URL: | https://d.repec.org/n?u=RePEc:grz:wpaper:2024-02 |
| By: | Jan-Henrik Steg (Bielefeld University, Germany); Elshan Garashli (University of Graz, Austria); Michael Greinecker (ENS Paris-Saclay, France); Christoph Kuzmics (University of Graz, Austria) |
| Abstract: | For cheap-talk games with a binary state space in which the sender has state-independent preferences, we characterize equilibria that are robust to introducing slight state-dependence on the side of the sender. Not all equilibria are robust, but the sender-optimum is always achieved at some robust equilibrium. |
| Keywords: | Cheap talk, Communication, Information transmission, Robustness. |
| JEL: | C72 D82 D83 |
| Date: | 2024–03 |
| URL: | https://d.repec.org/n?u=RePEc:grz:wpaper:2024-09 |
| By: | James C. Cox; Vjollca Sadiraj; James M. Walker |
| Abstract: | This paper studies the effect of power asymmetry on resolution of social dilemmas in repeated play of linear public good games. The experiment uses a 2X2 design that crosses power symmetry or asymmetry in payoff-equivalent provision and appropriation games with positive (provision) or negative (appropriation) externalities. Power asymmetry combines privileged access to information with extended opportunity sets that allow for taking a public good provided or not appropriated by others. Our data suggest that power asymmetry has a detrimental effect on efficiency, with the effect being more pronounced in the asymmetric-power appropriation game. Individual allocations to the public good increase in others' allocations, suggesting that individual allocations are not strategic substitutes. With power asymmetry, first movers earn less than the second mover in the appropriation game but not in the provision game. |
| JEL: | C73 C52 H41 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:exc:wpaper:2024-01 |
| By: | Anna Viktoria Rohrer (University of Graz, Austria); Santiago J. Rubio (University of Valencia, Spain) |
| Abstract: | This paper investigates the impact of the timing of adaptation on the stability of international environmental agreements (IEAs) for different levels of cooperation. This issue is addressed by solving a three-stage coalition formation game in a Nash-Cournot setting. In the first stage, countries decide non-cooperatively on their participation in an IEA. Then depending on the timing, countries decide on adaptation and emissions in the second and third stage. The game is solved for three levels of cooperation. Countries can either cooperate on emissions (emission agreement), on adaptation (adaptation agreement), or both actions (complete agreement). When emissions are chosen first, this extension to an emission-adaptation game is a generalization of the pure emission game. However, when adaptation is chosen first, the grand coalition is stable, provided that countries sign a complete agreement. With partial cooperation, stable coalitions are small. The results establish a connection between the strategic role of adaptation, the levels of adaptation of non-signatories and signatories for the different types of agreements and the participation in an IEA. Moreover, the results indicate that the grand coalition is stable even when it significantly enhances net benefits. |
| Keywords: | International Environmental Agreements, Emission-Adaptation Game, Prior Commitment, Strategic Effects, Participation, Effectiveness of Adaptation. |
| JEL: | D62 F53 H41 Q54 |
| Date: | 2023–03 |
| URL: | https://d.repec.org/n?u=RePEc:grz:wpaper:2023-03 |
| By: | Mario Gilli (Department of Economics, Management and Statistics, University of Milano-Bicocca); Andrea Sorrentino (Department of Economics, Management and Statistics, University of Milano-Bicocca) |
| Abstract: | We characterise the set of equilibria in a deterministic group contest with the weakest-link impact function, continuous efforts and a private good prize, complementing the results obtained by Chowdhury et al. (2016). We consider a two-stages two-groups model, where in the first stage the agents simultaneously choose the sharing rule, while in the second stage they choose efforts. Despite the existence of within-group symmetric Nash equilibria in pure strategies in the effort stage, there are combinations of possible sharing rules such that no pure strategy effort equilibria exist, hence for these sharing rules, the continuation payoffs are not defined, so that there exist no subgame perfect Nash equilibria in pure stragies. However, limiting ourselves to the restricted sharing rules case, we are able to state that there are continua of subgame perfect equilibria. In this case, by additional restrictions on the effort levels of each class of effort equilibria, we are able to computationally characterise the set of subgame perfect equilibria in pure strategies. |
| Keywords: | Group contests, sharing rules, indeterminacy |
| JEL: | D74 D71 C72 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:fem:femwpa:2024.21 |
| By: | Mario Gilli (Department of Economics, Management and Statistics, University of Milano-Bicocca); Andrea Sorrentino (Department of Economics, Management and Statistics, University of Milano-Bicocca) |
| Abstract: | In this paper we consider a deterministic complete information two groups contest where the effort choices made by the teammates are aggregated into group performance by the weakest-link technology (perfect complementarity), that is a “max-min group contest”, as defined by Chowdhury et al. (2016). However, instead of a continuum effort set, we employ a binary action set. Further, we consider private good prizes, so that there is a sharing issue within the winning group. Therefore, we include two stages: the first one about the setting of a sharing rule parameter and the second one about simultaneous and independent actions’ choices. The binary action set allow us to innovate on the existing literature by (i) characterizing the full set of the second stage equilibrium actions; (ii) computationally characterizing in MATLAB the set of within-group symmetric subgame perfect Nash equilibria in pure strategies in the entire game. We find conditions such that the set of within-group symmetric subgame perfect Nash equilibria in pure strategies have the cardinality of the continuum. We also check whether this paper’s results are due to discreteness or to binary choice, proving that in this case there are no subgame perfect Nash equilibria in pure strategies, as proved in the continuum case in Gilli and Sorrentino (2024). |
| Keywords: | Group contests, Sharing rules, Indeterminacy |
| JEL: | D74 D71 C72 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:fem:femwpa:2024.08 |
| By: | Davide Bosco (Department of Economics, Management and Statistics, University of Milano-Bicocca and Center for European Studies – CefES); Mario Gilli (Department of Economics, Management and Statistics, University of Milano-Bicocca, Milano and Center for European Studies – CefES) |
| Abstract: | We study effort provision and incentivisation in a Tullock group-contest with m = 2 groups that differ in size. A novel algorithmic procedure is presented that, under a symmetry assumption, explicitly characterises the equilibrium. Endogenous, optimal incentivisation schemes are then determined. Four results ensue. First, strategic interactions endogenously come in mean-field form: individual effort provision responds to the aggregate effort and average egalitarianism across groups. Therefore, the game is aggregative. Second, individuals endlessly cycle between zero and positive effort provision at some incentivisation schemes: no pure-strategy equilibria exist in these cases. Third, group size determines whether the egalitarianism of endogenous schemes increases or decreases in the average egalitarianism across groups. Fourth, all groups provide effort at the endogenous schemes if incentivisation is properly restricted. |
| Keywords: | Collective-action problem, Conflict, Selective incentives, Strategic complements and substitutes |
| JEL: | C72 D71 D74 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:fem:femwpa:2024.11 |
| By: | Piazolo, David; Vanberg, Christoph |
| Abstract: | We present a three-person, two-period bargaining game with private information. A single proposer is seeking to secure agreement to a proposal under either majority or unanimity rule. If the first period proposal fails, the game ends immediately with an exogenously given “breakdown” probability. Two responders have privately known disagreement payoffs. We characterize Bayesian equilibria in stagewise undominated strategies. Our central result is that responders have a signaling incentive to vote “no” on the first proposal under unanimity rule, whereas no such incentive exists under majority rule. The reason is that being perceived as a “high breakdown value type” is advantageous under unanimity rule, but disadvantageous under majority rule. As a consequence, responders are “more expensive” under unanimity rule and disagreement is more likely. These results confirm intuitions that have been stated informally before and in addition yield deeper insights into the underlying incentives and what they imply for optimal behavior in bargaining with private information. |
| Keywords: | Bargaining; voting; unanimity rule; majority rule; private information; signaling |
| Date: | 2024–07–27 |
| URL: | https://d.repec.org/n?u=RePEc:awi:wpaper:0753 |
| By: | Bart Taub |
| Abstract: | I examine strategic behaviour for a duopoly in a noisy environment. Firms attempt to learn the value of the rival’s privately observed demand shocks via a noisy signal of price, and at the same time firms attempt to obfuscate that signal by producing excess output on the publicly observable signals, that is, they signal jam. In a dynamic setting firms also distort the intertemporal structure of output keyed to the publicly observable demand shock process in order to disguise their private shocks. The net outcome is to radically increase the persistence of output over its full-information value. |
| Keywords: | Dynamic games, signal jamming, strategic information, frequency-domain methods. |
| JEL: | C61 C62 C63 C73 D43 D82 |
| Date: | 2023–01 |
| URL: | https://d.repec.org/n?u=RePEc:gla:glaewp:2023_02 |
| By: | Guillaume Bataille (AMSE); Benteng Zou (Departement of Economics and Management, University of Luxembourg) |
| Abstract: | Motivated by recent examples, this study proposes a dynamic multistage optimal control problem to explain the instability of International Fishery Agreements (IFAs). We model two heterogeneous countries that exploit shared fishery resources, and investigate the conditions that lead to a shift from cooperation to competition. We assume that countries differ in their time preferences, initially behave as if the coalition will last indefinitely, use fixed sharing rules during cooperation, and adopt Markovian strategies after withdrawal. Our findings reveal that, for any sharing rule, coalitions of heterogeneous players always break down in finite time. We use the dynamic Shapley Value to decompose the coalition’s aggregate worth over time, thereby eliminating the incentive to leave the agreement. Additionally, we show that a fishing moratorium policy accelerates the recovery of near-extinct fish stocks; however, fishing should resume under a cooperative regime once sustainable levels are achieved. |
| Keywords: | fisheries, International Fishery Agreements, Dynamic games, Multistage Optimal Control. |
| JEL: | C71 C72 Q22 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:aim:wpaimx:2421 |
| By: | Davidson, Marty |
| Abstract: | Spatial point processes provide a way for researchers to describe event-based outcomes in a bounded study window. Commonly used processes, such as the Neyman-Scott processes, however, often lack the behavioral frameworks that social scientists need to analyze strategic interactions between cohorts of actors. Strategic point processes address this issue by framing spatial point processes as a fixed set of players who engage in a countably infinite number of sequential games in a bounded study window. In this setup, each player receives a random function as their spatial strategy and their observed joint strategies generate the point pattern formations researchers record from the real world. To introduce the logic of strategic point processes, this paper describes the basic assumptions of Neyman-Scott (NS) spatial games, which model the clustering tendencies of strategic actors. Next, this paper discusses how researchers can reconstruct NS spatial games using observational datasets. Finally, this paper discusses how researchers can use complete spatial randomness (CSR) as an analytic baseline to draw inferences from NS spatial games. |
| Date: | 2024–07–08 |
| URL: | https://d.repec.org/n?u=RePEc:osf:osfxxx:g5r9t |
| By: | Franziska Flachsbarth; Anna Pechan; Martin Palovic; Matthias Koch; Dierk Bauknecht; Gert Brunekreeft |
| Abstract: | The electricity grid includes multiple network areas managed by different operators, with transmission system operators (TSOs) handling high-voltage areas and distribution system operators managing mid- to low-voltage areas. These areas are interconnected and synchronized, creating classical external effects where one operator's actions impact others. Recently, high voltage direct current (HVDC) lines have been introduced, offering operators greater flexibility and control over power flows compared to conventional alternating current (AC) lines, thereby reducing congestion and losses. However, HVDC lines can significantly affect neighbouring grids, potentially leading to strategic behaviour by network operators. This paper examines the strategic use of HVDC lines, using a model-based approach on projected 2030 market data in the German electricity system. It finds that without explicit coordination mechanisms most hours result in incentives for non-cooperative outcomes, with only three hours within one year showing incentives for a cooperative outcome. Despite lower overall system costs with cooperation, asymmetric distribution of cooperation benefits prevents long-term cooperation. Thus, cost-revenue- sharing schemes are needed to promote cooperation and balance benefits. |
| Keywords: | TSO coordination, strategic behaviour, game theory, simulation |
| JEL: | L51 L94 L43 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:bei:00bewp:0048 |
| By: | Zi Wang; Xingcheng Xu; Yanqing Yang; Xiaodong Zhu |
| Abstract: | We propose a deep learning framework, DL-opt, designed to efficiently solve for optimal policies in quantifiable general equilibrium trade models. DL-opt integrates (i) a nested fixed point (NFXP) formulation of the optimization problem, (ii) automatic implicit differentiation to enhance gradient descent for solving unilateral optimal policies, and (iii) a best-response dynamics approach for finding Nash equilibria. Utilizing DL-opt, we solve for non-cooperative tariffs and industrial subsidies across 7 economies and 44 sectors, incorporating sectoral external economies of scale. Our quantitative analysis reveals significant sectoral heterogeneity in Nash policies: Nash industrial subsidies increase with scale elasticities, whereas Nash tariffs decrease with trade elasticities. Moreover, we show that global dual competition, involving both tariffs and industrial subsidies, results in lower tariffs and higher welfare outcomes compared to a global tariff war. These findings highlight the importance of considering sectoral heterogeneity and policy combinations in understanding global economic competition. |
| Keywords: | Deep Learning; Tariff Wars; Industrial Policies; Optimal Policies; Nash Equilibria; Best-response dynamics; Quantitative Trade Models |
| JEL: | F12 F51 C61 C63 |
| Date: | 2024–07–24 |
| URL: | https://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-781 |
| By: | Eric Yan |
| Abstract: | We show the existence of mechanism design settings where the social planner has an interest in players receiving noisy signals about the types of other agents. When the social planner is interested only in partial implementation, any social choice rule that is incentive compatible after players receive additional information about other agents was originally incentive compatible prior to the change in information structure. However, information about other agents can eliminate undesired equilibria in an implementing mechanism. Thus, there are social choice rules which are not fully implementable in a given information environment that become fully implementable after players have additional information about the types of other agents. We provide some general conditions under which an undesired equilibrium can be eliminated by additional information about other players. |
| Date: | 2024–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.00037 |
| By: | Anton Kolotilin (School of Economics, UNSW Business School); Hongyi Li (School of Economics, UNSW Business School); Andriy Zapechelnyuk (School of Economics, University of Edinburgh) |
| Abstract: | We study monotone persuasion in the linear case, where a posterior distribution over states is summarized by its mean. We identify two settings where the optimal unrestricted signal can be nonmonotone. In the first setting, the optimal unrestricted signal requires randomization. In the second setting, the optimal unrestricted signal entails nonmonotone pooling of states. We solve for the optimal monotone signal in each setting, and illustrate our results with an application to media censorship. |
| Keywords: | Bayesian persuasion, monotone persuasion |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:swe:wpaper:2024-05 |
| By: | Condorelli, Daniele; Szentes, Balázs |
| Abstract: | We characterize equilibria of oligopolistic markets where identical rms with constant marginal cost compete a' la Cournot. For given maximal willingness to pay and maximal total demand, we rst identify all combinations of equilibrium consumer surplus and industry prot that can arise from arbitrary demand functions. Then, as a further restriction, we x the average willingness to pay above marginal cost (i.e., rst-best surplus) and identify all possible triples of consumer surplus, industry prot and deadweight loss. |
| Keywords: | Cournot; monopoly |
| JEL: | D42 D43 |
| Date: | 2022–08–03 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:111890 |
| By: | Park, Hyungmin (University of Warwick); Squintani, Francesco (University of Warwick) |
| Abstract: | We study the choice of multiple advisors, balancing political alignment, competence, and diverse perspectives. An imperfectly informed leader can consult one or two advisors. One has views closely aligned with the leader’s, but his information is imprecise or correlated with the leaders own. The other is more biased but has independent or more precise information. We identify a trade-off between consulting the more aligned or the better informed expert, even when this entails small costs. Subtle comparative statics emerge : When the leader consults both advisors, increasing the bias of the more biased expert may result in the dismissal of the other advisor. The leader may opt to delegate consulting and decision-making, but only to the advisor who collects superior information in equilibrium. We then study the uncertain trade-off case where the most informed advisor is not necessarily also more biased. We find that reducing the probability that the better-informed expert is more biased may lead to hiring also the other advisor. The leader may delegate to the advisor with uncertain bias, although he is more biased in expectation, because he more easily aggregates information in equilibrium. |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:wqapec:23 |
| By: | Jin Yeub Kim (Yonsei University); Jong Jae Lee (The Catholic University of Korea) |
| Abstract: | This paper presents a theory of mediator selection in conflicts that compares biased mediation and unbiased mediation. We determine when and how parties in dispute accept a biased mediator, and characterize optimal mechanisms used by biased mediators when they are selected into mediation in equilibrium. When asymmetric information is significant, parties accept biased mediation as long as the degree of mediator bias is not too high. Biased mediators care more about the payoffs of their favored party. Nevertheless, we find that biased mediators can be equally effective in promoting peace as the unbiased mediator. This implies that, once selected into mediation, the mediator’s effectiveness is independent of the degree of mediator bias. The key force of our results is that a biased mediator’s optimal recommendation strategies allocate more shares of resource to the favored party while providing a higher chance of a peaceful settlement to the disfavored party. |
| Keywords: | Biased Mediation, Conflict, Mechanism Design, Mediator Selection. |
| JEL: | C72 D74 D82 F51 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:yon:wpaper:2024rwp-230 |
| By: | Bontems, Philippe; Cheikbossian, Guillaume; Hafidi, Houda |
| Abstract: | This paper focuses on the welfare effects of domestic and international lobbying in the context of two countries linked by both trade and pollution. We consider a reciprocal-markets model where, in each country, a domestic firm produces a polluting good, that can result in a cross-national environmental externality, and competes in quantities in each market with a foreign firm. Each government independently sets a pollution tax under political pressure from green and industrial lobbies `a la Grossman and Helpman (1994). Our results mainly show that political pressure from domestic and/or international lobbies can help mitigate tax competition between the two countries, resulting in an improvement in social welfare. In fact, lobbying acts much like a strategic delegation device by changing the social welfare weights in the objective function of each government. The (potential) welfare-improving effect of political pressure depends on the relative strengths of the lobbies and on the nature of the strategic interactions in taxes. |
| Keywords: | Lobbying; transboundary pollution; international trade; international politics; environmental tax |
| JEL: | D72 F12 F18 Q58 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:129516 |
| By: | Juan C. Córdoba; Anni T. Isojärvi; Haoran Li |
| Abstract: | We document that the protracted decline in the labor share has been accompanied by a decline in the tightness rate defined as the number of vacancies per job seekers. We argue that these two trends are related. When vacancies and job seekers are complements in the matching process, a decline in the tightness rate reduces workers’ fundamental bargaining power as defined by Hosios (1990), which in turn reduces the labor share of income. We calibrate a search and matching model extended to allow for an endogenous determination of bargaining power. The model can rationalize the common trends in the labor shares and tightness. According to the model, workers’ bargaining power declined by about 15 percent during the 1980–2007 period. |
| Keywords: | CES matching function; Search and matching; Endogenous bargaining power; Labor share |
| JEL: | E25 J30 J50 |
| Date: | 2024–05–29 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedmoi:98592 |