|
on Game Theory |
| By: | Christian Ewerhart; Stanisław Kaźmierowski |
| Abstract: | Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the tie-breaking rule is allowed to be flexible. We begin by pointing out that equilibrium constructions known from the literature extend to our class of games. However, we also note that, irrespective of the tie-breaking rule, the equilibrium set is excessively large. Specifically, any pure strategy that allocates at most twice the fair share to each battlefield is used with positive probability in some equilibrium. Furthermore, refinements based on the elimination of weakly dominated strategies prove ineffective. To derive specific predictions amid this multiplicity, we compute strategies resulting from long-run adaptive learning. |
| Keywords: | Colonel Blotto games, multidimensional strategic reasoning, tiebreaking rules, Nash equilibrium, dominated strategies, adaptive learning |
| JEL: | C72 C91 D74 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:443&r=gth |
| By: | Hanchao Liu; Dena Firoozi |
| Abstract: | This paper presents a comprehensive study of Hilbert space-valued Linear-Quadratic-Gaussian (LQG) mean field games (MFGs), generalizing the classic LQG mean field game theory to scenarios where the state equations are driven by infinite-dimensional stochastic equations. In this framework, state and control processes take values in separable Hilbert spaces. Moreover, the state equations involve infinite dimensional noises, namely $Q$-Wiener processes. All agents are coupled through the average state of the population appearing in their linear dynamics and quadratic cost functional. In addition, the diffusion coefficient of each agent involves the state, control, and the average state processes. We first study the well-posedness of a system of coupled infinite-dimensional stochastic evolution equations, which forms the foundation of MFGs in Hilbert spaces. Next, we develop the Nash Certainty Equivalence principle and obtain a unique Nash equilibrium for the limiting Hilbert space-valued MFG. Finally, we establish the $\epsilon$-Nash property for the finite-player game in Hilbert space. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.01012&r=gth |
| By: | Clinton Gabon Gassi (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France) |
| Abstract: | We consider cooperative games where the coalition structure is given by the set of winning coalitions of a simple game. This type of games models some real-life situations in which some agents have economic performances while some others are endowed with a political power. On this class of cooperative games, the Myerson value has been identified as the Harsanyi power solution associated to the Equal Division power index and has been characterized in the large class of Harsanyi power solutions with respect to the associated power index. In this paper, we provide a characterization of the Myerson value for this class of games without focusing on the whole family of Harsanyi power solutions and therefore, without taking into account any power index. We identify the Myerson value as the only allocation rule that satisfies efficiency, additivity, modularity, extra-null player property, and Equal Treatment of Veto. |
| Keywords: | TU-game, Voting structure, Harsanyi dividends, Harsanyi power solution, Myerson value. |
| JEL: | D71 D72 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2024-10&r=gth |
| By: | Francesco De Sinopoli; Leo Ferraris; Claudia Meroni |
| Abstract: | In a coordination game with multiple Pareto ordered equilibria and population uncertainty, we show that group size helps select a unique equilibrium, for reasons reminiscent of the global games literature. A critical mass phenomenon emerges at equilibrium. Group size has an emboldening effect on participants. |
| Keywords: | Poisson Games, Coordination Games, Equilibrium Selection, Global Games |
| JEL: | C72 D82 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:mib:wpaper:533&r=gth |
| By: | Jozsef Konczer |
| Abstract: | This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are connected to Frequentist and Bayesian statistics, respectively. Later, a more general type of game is introduced, termed Statistical game, in which a further parameter, the players' relative risk aversion, can be set. In this work, we show that Fisher and Bayesian games can be viewed as limiting cases of Statistical games. Therefore, Statistical games can be viewed as a unified framework, incorporating both Frequentist and Bayesian statistics. Furthermore, a philosophical framework is (re-)presented -- often referred to as minimax regret criterion -- as a general approach to decision making. The main motivation for this work was to embed Bayesian statistics into a broader decision-making framework, where, based on collected data, actions with consequences have to be made, which can be translated to utilities (or rewards/losses) of the decision-maker. The work starts with the simplest possible toy model, related to hypothesis testing and statistical inference. This choice has two main benefits: i.) it allows us to determine (conjecture) the behaviour of the equilibrium strategies in various limiting cases ii.) this way, we can introduce Statistical games without requiring additional stochastic parameters. The work contains game theoretical methods related to two-player, non-cooperative games to determine and prove equilibrium strategies of Fisher, Bayesian and Statistical games. It also relies on analytical tools for derivations concerning various limiting cases. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.15892&r=gth |
| By: | Ponthiere, Gregory |
| Abstract: | This paper revisits the Tragedy of the Commons - a Pareto-dominated overuse of a common resource - through the lenses of Stoicism, and, in particular, of the Stoic discipline of desires, according to which one should wish for nothing that is not under one's control. When the Stoic discipline of desires is modelled as a requirement of indifference between outcomes differing only on things out of control, Stoic agents are shown not to overuse the common resource. Alternatively, when the Stoic discipline of desires requires indifference between best outcomes under each circum- stance, the Nash equilibrium, if it exists, cannot be Pareto-dominated. Depending on how the Stoic discipline of desires is formalized, a recen- tering of agents towards things under their control either allows them to avoid overusing the commons, or makes the use of commons not "tragic". |
| Keywords: | Tragedy of the Commons, Stoicism, rationality, common resource game, land overuse |
| JEL: | Q24 D62 D91 Z1 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:glodps:1405&r=gth |
| By: | Francesc Dilmé (University of Bonn) |
| Abstract: | This paper studies bargaining between a seller and a buyer with binary private valuation. Because the setting is more tractable than the case of general valuation distributions (studied in Gul et al., 1986), we are able to explicitly construct the full set of equilibria via induction. This lets us provide a simple proof of the Coase conjecture and obtain new results: The seller extracts all surplus as she becomes more patient, and the equilibrium outcome converges to the perfect-information outcome as private information vanishes. We also fully characterize the case where there is a deadline: We establish that if the probability that the buyer’s valuation is high is large enough, then the seller charges a high price at all times, there are trade bursts at the outset and the deadline, and trade occurs at a constant rate in between. |
| Keywords: | Bargaining, private information, one-sided offers |
| JEL: | C78 D82 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:ajk:ajkdps:284&r=gth |
| By: | Papatya Duman (Paderborn University); Claus-Jochen Haake (Paderborn University) |
| Abstract: | We investigate whether the recently approved reforms of the apportionment of parliamentary seats to parties in the German Bundestag affects the parties’ political influence measured by power indices. We find that under neither reform the underlying simple game, which describes the possibilities to form governments, remains unchanged and as a result the Shapley-Shubik and the Banzhaf index are unaltered. As a consequence, the major change from the reforms is the size reduction in the Bundestag by currently 106 legislators to 630. |
| Keywords: | Reform Bundestag, Banzhaf power index, Shapley-Shubik power index |
| JEL: | D72 C71 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:ciepap:158&r=gth |
| By: | Gächter, Simon (University of Nottingham); Lee, Kyeongtae (Bank of Korea); Sefton, Martin (University of Nottingham); Weber, Till O. (Newcastle University) |
| Abstract: | The prisoner's dilemma (PD) is arguably the most important model of social dilemmas, but our knowledge about how a PD's material payoff structure affects cooperation is incomplete. In this paper we investigate the effect of variation in material payoffs on cooperation, focusing on one-shot PD games where efficiency requires mutual cooperation. We report results from three experiments (N = 1, 993): in a preliminary experiment, we vary the payoffs over a large range. In our first main experiment (Study 1), we present a novel design that varies payoffs orthogonally in a within-subjects design. Our second main experiment, Study 2, investigates the orthogonal variation of payoffs in a between-subjects design. In a complementary analysis we also study the closely related payoff indices of normalized loss and gain, and the K-index. The most robust finding of our experiments and the complementary analyses is that cooperation in a PD increases with the gains of mutual cooperation over mutual defection. |
| Keywords: | prisoner's dilemma, cooperation, payoff parameters, temptation, risk, efficiency, normalized gain, normalized loss, K-index, experiments |
| JEL: | A13 C91 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp16814&r=gth |
| By: | Rupayan Pal (Indira Gandhi Institute of Development Research); Emmanuel Petrakis (Departamento de Econom¡a, Universidad Carlos III de Madrid) |
| Abstract: | This paper shows that in a duopoly a firm has no incentives to divest its passive shares in its rival when firms' strategies are strategic complements. This holds independently whether goods are substitutes or complements and whether firms engage in simultaneous or sequential move product market competition. However, if firms' strategies are strategic substitutes and are engaged in simultaneous move competition, it is optimal for both firms to fully divest their shares in their rivals under a private placement mechanism via independent intermediaries or under competitive bidding. Yet, in the sequential move game only the follower has such incentives. Notably, under a private placement mechanism via a common intermediary, there are circumstances under which there are partial or no firms' divestment incentives, highlighting that the divestment mechanism employed by firms may have a crucial role on their divestment incentives. |
| Keywords: | Cross-ownership, passive shares, strategic substitutes and complements, divestment incentives, market competition |
| JEL: | L13 L41 L2 D43 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:ind:igiwpp:2024-003&r=gth |
| By: | Ahmed S. Alahmed; Guido Cavraro; Andrey Bernstein; Lang Tong |
| Abstract: | We propose an operating envelopes (OEs) aware energy community market mechanism that dynamically charges/rewards its members based on two-part pricing. The OEs are imposed exogenously by a regulated distribution system operator (DSO) on the energy community's revenue meter that is subject to a generalized net energy metering (NEM) tariff design. By formulating the interaction of the community manager and its members as a Stackelberg game, we show that the proposed two-part pricing achieves a Nash equilibrium and maximizes the community's social welfare in a decentralized fashion while ensuring that the community's operation abides by the OEs. The market mechanism conforms with the cost-causation principle and guarantees community members a surplus level no less than their maximum surplus when they autonomously face the DSO. The dynamic and uniform community price is a monotonically decreasing function of the community's aggregate renewable generation. We also analyze the impact of exogenous parameters such as NEM rates and OEs on the value of joining the community. Lastly, through numerical studies, we showcase the community's welfare, pricing, and compare its members' surplus to customers under the DSO and other OEs arrangements. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.17201&r=gth |
| By: | Alfred Galichon; Antoine Jacquet |
| Abstract: | Matching problems with linearly transferable utility (LTU) generalize the well-studied transferable utility (TU) case by relaxing the assumption that utility is transferred one-for-one within matched pairs. We show that LTU matching problems can be reframed as nonzero-sum games between two players, thus generalizing a result from von Neumann. The underlying linear programming structure of TU matching problems, however, is lost when moving to LTU. These results draw a new bridge between non-TU matching problems and the theory of bimatrix games, with consequences notably regarding the computation of stable outcomes. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.12200&r=gth |
| By: | Niharika Kakoty; Surajit Borkotokey; Rajnish Kumar; Abhijit Bora |
| Abstract: | We study the weighted Myerson value for Network games extending a similar concept for communication situations. Network games, unlike communication situations, treat direct and indirect links among players differently and distinguish their effects in both worth generation and allocation processes. The weighted Myerson value is an allocation rule for Network games that generalizes the Myerson value of Network games. Here, the players are assumed to have some weights measuring their capacity to form links with other players. Two characterization of the weighted Myerson value are provided. Finally, we propose a bidding mechanism to show that the weighted Myerson value is a subgame-perfect Nash equilibrium under a non-cooperative framework. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.11464&r=gth |
| By: | Warnes, Xavier Sebastian (Stanford U); de Zegher, Joann F. (MIT); Iancu, Dan A. (Stanford U); Plambeck, Erica (Stanford U) |
| Abstract: | Tropical deforestation for agriculture causes alarming CO2 emissions and loss of biodiversity and ecosystem services. To prevent this, various governments and multinational commodity-buyers offer a positive incentive for locals conditional on no deforestation in a specified area. As an alternative to the area no-deforestation condition, we propose a weaker "regeneration condition": if forest is cleared on land in the specified area, locals prevent its economic use, enabling the forest to regenerate. With innovation in cooperative game theory, we characterize the best condition (area no-deforestation vs. area regeneration) and feasible incentives to prevent deforestation and to compensate each local for his missed economic opportunity. The regeneration condition is best in an area with the potential for entrants to engage in deforestation. Without entrants, if locals can cooperate, the area no-deforestation condition is best, and works with any incentive that is more valuable for locals collectively than deforestation. By surveying smallholder palm farmers in 58 villages of East Kalimantan, Indonesia, we fit our model with a price premium for palm fruit as the incentive, in each village as the area. A price premium is an imperfect incentive, having least value for a farmer with the least land and, correspondingly, high temptation to engage in deforestation. The Roundtable on Sustainable Palm Oil (RSPO) price premium is too low. Still, with a moderate price premium, our area regeneration condition prevents deforestation in most villages and is remarkably robust to deter potential entrants. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:4143&r=gth |
| By: | Lisa Bruttel (University of Potsdam, CEPA); Vasilisa Petrishcheva (University of Potsdam) |
| Abstract: | In this paper, we study one channel through which communication may facilitate cooperative behavior – belief precision. In a prisoner’s dilemma experiment, we show that communication not only makes individuals more optimistic that their partner will cooperate but also increases the precision of this belief, thereby reducing strategic uncertainty. To disentangle the shift in mean beliefs from the increase in precision, we elicit beliefs and precision in a two-stage procedure and in three situations: without communication, before communication, and after communication. We find that the precision of beliefs increases during communication. |
| Keywords: | prisoner’s dilemma, communication, beliefs, strategic uncertainty, experiment |
| JEL: | C92 D83 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:pot:cepadp:74&r=gth |
| By: | Rumen Kostadinov |
| Abstract: | I study a dynamic model of durable-good monopoly where the seller cannot commit to future prices and is uncertain about the buyer’s value. I adopt a prior-free approach where the seller minimises lifetime regret against the worstcase type of the buyer. In the unique equilibrium the seller’s worst-case regret against types who purchase at any given time equals the worst-case regret against types who purchase at any other time. The seller cannot profitably deviate even if he could commit to his deviation. Despite this, the equilibrium does not match the commitment outcome. This is because the seller’s objective is endogenously determined by his optimal counterfactual behaviour against each type, which is time-inconsistent. The Coase conjecture holds: in the frequent-offer limit the good is sold immediately at a price equal to the lowest value. |
| Keywords: | durable-good monopoly; Coase conjecture; regret |
| JEL: | C73 D81 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:mcm:deptwp:2024-02&r=gth |
| By: | Harstad, Bard (Stanford U) |
| Abstract: | International trade and natural resource exploitation interact in multiple ways. This paper first presents a dynamic game in which the South (S) exploits (e.g., deforests) in order to export (e.g., lumber or agricultural products). Because of negative externalities, the North might lose from trade, unless the resource has already been depleted. Anticipating this, S exploits more. All negative results are reversed if renegotiation-proof tariffs can be contingent on the size of the remaining resource stock. Larger gains from trade, and more attractive terms of trade, can be used to slow exploitation. Combined with export subsidies, the outcome is first best. |
| JEL: | F13 F18 F55 Q37 Q56 |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:4127&r=gth |
| By: | David K Levine |
| Date: | 2024–03–14 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:786969000000001843&r=gth |
| By: | Oumar Mbodji; Traian A. Pirvu |
| Abstract: | Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider the subgame perfect strategies. The later are characterized through an extended Hamilton Jacobi Bellman (HJB) equation. A fixed point iteration is employed to solve the extended HJB equation. This is done in a two stage approach: in a first step the utility weighted discount rate is introduced and characterized as the fixed point of a certain operator; in the second step the value function is determined through a linear parabolic partial differential equation. Numerical experiments explore the effect of the time discount rate on the subgame perfect and precommitment strategies. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.05113&r=gth |