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on Game Theory |
| By: | Jens Gudmundsson; Jens Leth Hougaard; Jay Sethuraman |
| Abstract: | Interconnected agents such as firms in a supply chain make simultaneous preparatory investments to increase chances of honouring their respective bilateral agreements. Failures cascade: if one fails their agreement, then so do all who follow in the chain. Thus, later agents' investments turn out to be pointless when there is an earlier failure. How losses are shared affects how agents invest to avoid the losses in the first place. In this way, a solution sets agent liabilities depending on the point of disruption and induces a supermodular investment game. We characterize all efficient solutions. These have the form that later agents -- who are not directly liable for the disruption -- still shoulder some of the losses, justified on the premise that they might have failed anyway. Importantly, we find that such indirect liabilities are necessary to avoid unbounded inefficiencies. Finally, we pinpoint one efficient solution with several desirable properties. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.07361 |
| By: | Hana Krakovsk\'a; Rudolf Hanel; Mark Broom |
| Abstract: | The Ultimatum Game is conventionally formulated in the context of two players. Nonetheless, real-life scenarios often entail community interactions among numerous individuals. To address this, we introduce an extended version of the Ultimatum Game, called the Multi-Proposer-Multi-Responder Ultimatum Game. In this model, multiple responders and proposers simultaneously interact in a one-shot game, introducing competition both within proposers and within responders. We derive subgame-perfect Nash equilibria for all scenarios and explore how these non-trivial values might provide insight into proposal and rejection behavior experimentally observed in the context of one vs. one Ultimatum Game scenarios. Additionally, by considering the asymptotic numbers of players, we propose two potential estimates for a "fair" threshold: either 31.8% or 36.8% of the pie (share) for the responder. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.02410 |
| By: | Nicolas Schutz |
| Abstract: | I study a model in which two upstream firms compete to supply a homogeneous input to two downstream firms selling differentiated products. Upstream firms offer exclusive, discriminatory, public, two-part tariff contracts to the downstream firms. I show that, under very general conditions, this game does not have a pure-strategy subgame-perfect equilibrium. The intuition is that variable parts in such an equilibrium would have to be pairwise-stable; however, with pairwise-stable variable parts, downstream competitive externalities are not internalized, implying that upstream firms can profitably deviate. I contrast this non-existence result with earlier papers that found equilibria in related models. |
| Keywords: | vertical relations, exclusive dealing, two-part tariffs, slotting fees. |
| JEL: | L13 L14 L42 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_591 |
| By: | Juan Pablo Rinc\'on-Zapatero |
| Abstract: | We analyze the question of whether the outcome of an oligopoly exploiting a nonrenewable resource can be replicated by a related monopoly, within the framework of continuous time and Markov Perfect Nash Equilibrium. We establish necessary and sufficient conditions and find explicit solutions in some cases. Also, very simple models with externalities are shown which Nash equilibrium cannot be replicated in a monopoly. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.20810 |
| By: | Zola, Maurizio Angelo |
| Abstract: | The classical mixed strategies non-cooperative solution of a two person – two move game is recalled by paying attention to the different proposed methods and to the properties of the so found solutions. The non-cooperative equilibrium point is determined by a new geometric approach based on the dominance principle. Starting from the algebraic bi-linear form of the expected payoffs of the two players in the( x, y) domain of the probabilistic distribution on the pure strategies, the two equations are studied as surfaces in the 3D space on the basis of the sound theory of the quadratic forms. The study of the properties of the quadric is performed by classifying the bi-linear form as pertaining to a classical hyperbolic paraboloid and the relationship between its geometric properties and the probabilistic distribution on the pure strategies is found. The application of the dominance principle allows to choose the equilibrium point among the classical solutions avoiding the ambiguity due to their non-interchangeability and a conjecture about the uniqueness of the solution is proposed in order to solve the problem of the existence and uniqueness of the noncooperative solution of a two-by-two game. The uniqueness of the non-cooperative solution could be used as a starting point to find out the cooperative solution of the game too. |
| Keywords: | Dominance principle; General sum game; two person-two move game |
| JEL: | C72 |
| Date: | 2024–04–29 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121763 |
| By: | Lu Yu |
| Abstract: | We give two generalizations of the Zhou fixed point theorem. They weaken the subcompleteness condition of values, and relax the ascending condition of the correspondence. As an application, we derive a generalization of Topkis's theorem on the existence and order structure of the set of Nash equilibria of supermodular games. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.17884 |
| By: | Gabriele Camera; Alessandro Gioffré |
| Abstract: | The literature on cooperation in infinitely repeated Prisoner’s Dilemmas covers the extreme opposites of the matching spectrum: partners, a player’s opponent never changes, and strangers, a player’s opponent randomly changes in every period. Here, we extend the analysis to settings where the opponent changes, but not in every period. In these temporary partnerships, players can deter some deviations by directly sanctioning their partner. Hence, relaxing the extreme assumption of one-period matchings can support some cooperation also off equilibrium because a class of strategies emerges that are less extreme than the typical “grim†strategy. We establish conditions supporting full cooperation as a subgame perfect equilibrium under a social norm that complements direct sanctions with a cyclical community sanction. Though this strategy less effectively incentivizes cooperation, it more effectively incentivizes punishment after a deviation, hence, can be preferable to the grim strategy under certain conditions. |
| Keywords: | prisoner's dilemma, random matching, social norms. |
| JEL: | E4 E5 C7 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:frz:wpaper:wp2024_15.rdf |
| By: | Giorgio Calcagnini; Germana Giombini; Edgar J. Sanchez Carrera |
| Abstract: | We consider a green monetary policy framework implemented by the central bank. Under this framework, firms and commercial banks decide whether or not to apply a green (environmentally friendly) or brown (conventional) investment and policy, respectively. We develop an evolutionary game to study the conditions under which a stable or unstable equilibrium is reached. If the green firms' revenues minus their bank loans and their transition costs are strictly greater than the brown firms' revenues and their pollution costs, together with (primary or subsidized) green interest rates such that the default risk is lower for green firms compared to brown ones, then the economy evolves to a asymptotically stable green state. In the green state all banks give green loans and all firms invest in green investment. If the condition is reversed the economy converges to a brown state. If the banks and the firms are indifferent towards the green and brown policy and investment respectively, the economy fluctuates from green to brown state. There may be multiple equilibria. Through a transcritical bifurcation we show how stability (instability) of the equilibria changes with the parameters. |
| Keywords: | Climate Change; Evolutionary Dynamics; Green monetary policies; Firms Pollution |
| JEL: | C70 C72 D21 K42 L21 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:frz:wpaper:wp2024_16.rdf |
| By: | Appelbaum, Elie; Anam, Mahmudul; Chiang, Shin-Hwan |
| Abstract: | Using a simple duopolistic trade model with demand uncertainty and an identical traded product, we show that we can view trade in goods as implicit exports/imports of risk and risk aversion. Specifically, we show that a relatively “risk-aversion abundant” country is more likely to be a net importer of the product – hence an importer of low risk-aversion. Similarly, a “relatively high-risk abundant” country is more likely to be the net exporter of the product - hence an importer of low risk. We also show that market correlations and differences in risk aversion and risk are sources of implicit risk-sharing and diversification gains from trade. Consequently, the relatively high-risk or high-risk-aversion country always gains from trade, whereas the other country will most likely gain unless markets are highly positively correlated. Furthermore, we re-examine the (Brander-Spencer) strategic export subsidy game in the context of uncertainty and find that because both efficient risk management and rent shifting need to be considered, contrary to conventional wisdom, the equilibrium policy regime may be an export tax rather than a subsidy. |
| Keywords: | Patterns of Trade; Gains from Trade; Risk;Risk Aversion; Exports; Subsidies. |
| JEL: | D81 F12 F13 F15 |
| Date: | 2024–07–28 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121605 |
| By: | Jens Gudmundsson (University of Copenhagen); Jens Leth Hougaard (University of Copenhagen); Erik Ansink (Vrije Universiteit Amsterdam) |
| Abstract: | We take a decentralized approach to regulating environmental pollution in set- tings where each agent’s pollution possibly affects all others. There is no central agency to enforce pollution abatement or coordinate monetary transfers. Moreover, agents possess private information, which precludes deducing efficient abatement in general. We propose to implement transfer schemes through smart contracts to allow beneficiaries to compensate for abatement. We characterize all schemes that induce efficient abatement in unique dominant-strategy equilibrium. Moreover, appealing to classical fairness tenets, we pin down the “beneficiaries-compensates principle†. Supporting this principle through smart contracts provides a promising step towards decentralized coordination on environmental issues. |
| Keywords: | Pollution, Decentralization, Smart contracts, Beneficiaries-compensates principle |
| JEL: | C72 D62 Q52 H23 |
| Date: | 2024–05–23 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240035 |
| By: | Wassim Daher (Gulf University for Science and Technology, Kuwait); Jihad Elnaboulsi (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France); Mahelet G. Fikru (Missouri University of Science and Technology, USA); Luis Gautier (Universidad de Málaga, Spain) |
| Abstract: | We study the incentives to merge for energy producers in the presence of distributed renewable energy producers. Utilizing a Cournot model, we explore how uncertainty surrounding the cost of grid integration influences the profitability of mergers, where uncertainty comes in the form of an industry-wide shock (or common) and firm-specific errors (private shock). We find that the effect of these uncertainties on merger profitability depends on average energy grid integration costs, the size of the merger, and quality of private information. Overall, results suggest that mergers are more likely to be profitable when firms can effectively absorb private shocks due to the scale of the merger, unless average grid integration costs become too high. The incentives to merge are less clear-cut in the presence of an industry-wide shock, unless the quality of private information is high enough. |
| Keywords: | - |
| JEL: | Q4 G34 Q2 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:crb:wpaper:2024-14 |