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on Game Theory |
| By: | Juli\'an Chitiva; Xavier Venel |
| Abstract: | We develop an extension of the classical model of DeGroot (1974) to a continuum of agents when they interact among them according to a DiKernel $W$. We show that, under some regularity assumptions, the continuous model is the limit case of the discrete one. We provide some applications of this result. First, we establish a canonical way to reduce the dimensionality of matrices by comparing matrices of different dimensions in the space of DiKernels. Then, we develop a model of Lobby Competition where two lobbies compete to bias the opinion of a continuum of agents. We give sufficient conditions for the existence of a Nash Equilibrium. Furthermore, we establish the conditions under which a Nash Equilibrium of the game induce an $\varepsilon$-Nash Equilibrium of the discretization of the game. Finally, we put forward some elements for the characterization of equilibrium strategies. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.11710 |
| By: | Ricardo Martinez; Juan D. Moreno-Ternero |
| Abstract: | We take an axiomatic approach to the allocation of riparian water rights. We formalize ethical or structural properties as axioms of allocation rules. We show that several combinations of these axioms characterize focal rules implementing the principle of Territorial Integration of all Basin States in various forms. One of them connects to the Shapley value, the long-standing centerpiece of cooperative game theory. The others offer natural compromises between the polar principles of Absolute Territorial Sovereignty and Unlimited Territorial Integrity. We complete our study with an empirical application to the allocation of riparian water rights in the Nile River. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.14623 |
| By: | \'Alvaro Cartea; Sebastian Jaimungal; Leandro S\'anchez-Betancourt |
| Abstract: | We study the perfect information Nash equilibrium between a broker and her clients -- an informed trader, and an uniformed trader. In our model, the broker trades in the lit exchange where trades have instantaneous and transient price impact with exponential resilience, while both clients trade with the broker. The informed trader and the broker maximise expected wealth subject to inventory penalties, while the uninformed trader is not strategic and sends the broker random buy and sell orders. We characterise the Nash equilibrium of the trading strategies with the solution to a coupled system of forward-backward stochastic differential equations (FBSDEs). We solve this system explicitly and study the effect of information in the trading strategies of the broker and the informed trader. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.10561 |
| By: | Gianmarco Del Sarto; Marta Leocata; Giulia Livieri |
| Abstract: | We develop a model based on mean-field games of competitive firms producing similar goods according to a standard AK model with a depreciation rate of capital generating pollution as a byproduct. Our analysis focuses on the widely-used cap-and-trade pollution regulation. Under this regulation, firms have the flexibility to respond by implementing pollution abatement, reducing output, and participating in emission trading, while a regulator dynamically allocates emission allowances to each firm. The resulting mean-field game is of linear quadratic type and equivalent to a mean-field type control problem, i.e., it is a potential game. We find explicit solutions to this problem through the solutions to differential equations of Riccati type. Further, we investigate the carbon emission equilibrium price that satisfies the market clearing condition and find a specific form of FBSDE of McKean-Vlasov type with common noise. The solution to this equation provides an approximate equilibrium price. Additionally, we demonstrate that the degree of competition is vital in determining the economic consequences of pollution regulation. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.12754 |
| By: | Guillaume Bataille (Aix Marseille Université); Benteng Zou (DEM, Université du 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 |
| URL: | https://d.repec.org/n?u=RePEc:luc:wpaper:24-06 |
| By: | David M. Kryskowski; David Kryskowski |
| Abstract: | This paper expands on the concepts presented in Applying the Nash Bargaining Solution for a Reasonable Royalty ( arXiv:2005.10158 ). The goal is to refine the process for determining a reasonable royalty using statistical methods in cases where there is risk and uncertainty regarding each party's disagreement payoffs (opportunity costs) in the Nash Bargaining Solution (NBS). This paper uses a Bayes Cost approach to analyze Case 1, Case 2, and the Original Nash model from the authors' previous work. By addressing risk and uncertainty in the NBS, the NBS emerges as a more reliable method for estimating a reasonable royalty, aligning with the criteria outlined in Georgia Pacific factor fifteen. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.14642 |
| By: | Deepal Basak; Joyee Deb; Aditya Kuvalekar |
| Abstract: | We study a canonical collective action game with incomplete information. Individuals attempt to coordinate to achieve a shared goal, while also facing a temptation to free-ride. Consuming more similar information about the fundamentals can help them coordinate, but it can also exacerbate free-riding. Our main result shows that more similar information facilitates (impedes) achieving a common goal when achieving the goal is sufficiently challenging (easy). We apply this insight to show why insufficiently powerful authoritarian governments may face larger protests when attempting to restrict press freedom, and why informational diversity in committees is beneficial when each vote carries more weight. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.14773 |
| By: | Cappelli, Veronica Roberta (Santa Fe Institute); Chatain, Olivier (HEC Paris) |
| Abstract: | How to extend the use of value-based strategy models to situations with large quasi-rents shared among multiple actors, such as ecosystems? How to consider how players understand competition in value-based models? How to overcome some limitations of these models such as lack of uniqueness of solutions? In this paper, we extend the reach of value-based strategy by revisiting the celebrated biform games model to answer these questions. Operationally, we make players evaluate their payoff from the cooperative stage of the game according to a generalized expectation over their value capture. Our solution has several advantages: (i) It subsumes the original biform framework and seamlessly integrates recent works providing bounds to value capture (ii) It allows solving issues such as the possible non-uniqueness of solutions and invariance to the competitive environment structure while maintaining the role of competition in determining value capture (iii) It remains axiomatically justified on behavioral grounds (iv) It permits richer preferences representations that, for example, can include subjective distortions of objective chances of value capture (v) It further leads the way to the use of generalized preference representations in the value-based framework. |
| Keywords: | value-based strategy; value-base models; |
| JEL: | L00 |
| Date: | 2023–01–05 |
| URL: | https://d.repec.org/n?u=RePEc:ebg:heccah:1464 |
| By: | Afiq bin Oslan |
| Abstract: | Border fortifications have proliferated in recent decades. One prominent rationale given for fortifying the border is to limit illegal incursions, but how successful are fortifications at this task? Current theories fail to account for the fact that illicit actors may be strategic in their choices in order to influence state policies. I accommodate this strategic behaviour in a formal model to demonstrate that this capacity for strategy means that border fortifications are rarely optimal. In the model, states can learn the capacities of illicit actors through the latter’s past transgressions to inform border security policy. Anticipating this, illicit actors may moderate their actions to discourage fortifications. States therefore only secure their borders when illicit actors are powerful enough such that the threat of fortifications does not deter them into moderation. This reveals an inefficiency in border security that gives new insight into the dynamics of border politics. |
| Keywords: | Border Politics, Border Policy, Game Theory, Illicit Trade |
| URL: | https://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2023-18 |
| By: | Leal, Alan (Ph.D. candidate in Economics at Universidade of São Paulo); Bugarin, Maurício (Full Professor of Economics at University of Brasília) |
| Abstract: | Trade and environment are intertwined subjects. The literature on the impact of trade opening on environmental outcomes are vast. Lacking however is the literature in how trade can be used politically to induce better environmental outcomes. To model this properly, we develop a game theoretic model in which two countries engage in trade and choose their respective levels of deforestation and trade tariffs. We consider the scenarios of market and central equilibria and derive some useful insights into their relationship of these two variables. As an extension, we also propose different model specifications and develop a numeric generalization of the model, which allows testing our models prediction for several countries. As a result, we find that there is an incentive for free-riding from the countries less concerned with deforestation on the countries that suffer the most disutility of its own deforestation. |
| Keywords: | trade; deforestation; game theory |
| JEL: | F10 |
| Date: | 2024–08–02 |
| URL: | https://d.repec.org/n?u=RePEc:ris:nereus:2024_005 |
| By: | Patrick Allmis |
| Abstract: | Agents with different ideologies often form alliances to achieve their goals. Paradoxically, ideologically similar agents are often opponents. In this paper, ideologically heterogeneous agents choose the ideological composition of their neighborhood, their tolerance, and invest into connections. The resulting weighted network describes allies, opponents, and strengths. Disputes with opponents determine benefits, which increase in an agent's strength and cohesion. Cohesive agents have fewer mutual allies with opponents. In equilibrium, the network is segregated when cohesion is effective enough and some agents tolerate ideologically distant types to oppose closer ones. Subsidizing connections dampens polarization in societies on the verge of segregation. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.14045 |
| By: | Mingyang Li; Maoqin Yuan; Han Pengsihua; Yuan Yuan; Zejun Wang |
| Abstract: | This study investigates the potential impact of "LK-99, " a novel material developed by a Korean research team, on the power equipment industry. Using evolutionary game theory, the interactions between governmental subsidies and technology adoption by power companies are modeled. A key innovation of this research is the introduction of sensitivity analyses concerning time delays and initial subsidy amounts, which significantly influence the strategic decisions of both government and corporate entities. The findings indicate that these factors are critical in determining the rate of technology adoption and the efficiency of the market as a whole. Due to existing data limitations, the study offers a broad overview of likely trends and recommends the inclusion of real-world data for more precise modeling once the material demonstrates room-temperature superconducting characteristics. The research contributes foundational insights valuable for future policy design and has significant implications for advancing the understanding of technology adoption and market dynamics. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.01017 |
| By: | Aner Sela (BGU); Ishay Rabi (BGU); Chen Cohen (BGU) |
| Keywords: | Parallel contests; reputation; heterogenous agents, non-linear e ort costs |
| JEL: | D44 D72 D82 J31 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:bgu:wpaper:2409 |
| By: | Paul S. Koh |
| Abstract: | Market definition holds significant importance in antitrust cases, yet achieving consensus on the correct approach remains elusive. As a result, analysts routinely entertain multiple market definitions to ensure the resilience of their conclusions. I propose a simple framework for conducting organized sensitivity analysis with respect to market definition. I model candidate market definitions as partially ordered and use a Hasse diagram, a directed acyclic graph representing a finite partial order, to summarize the sensitivity analysis. I use the Shapley value and the Shapley-Shubik power index to quantify the average marginal contribution of each firm in driving the conclusion. I illustrate the method's usefulness with an application to the Albertsons/Safeway (2015) merger. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.12774 |
| By: | Anastasia Danilov; Ju Yeong Hong; Anja Schöttner |
| Abstract: | A significant portion of the workforce experiences what we term `unfriendly leadership, ' encompassing various forms of hostile behavior exhibited by managers. The motivations driving managers to adopt such behaviors are insufficiently understood. To explore this phenomenon, we conducted a laboratory experiment examining the relationship between managers' use of unfriendly leadership and labor market competition. We discern two labor market states: excess labor demand, where managers compete to hire workers, and excess labor supply, where workers compete to be hired. By perceiving unfriendly leadership as a performance-contingent punishment device inflicting discomfort on workers, we hypothesize that managers are less inclined to resort to unfriendly leadership when they compete to hire workers. We find that managers tend to engage in unfriendly leadership more frequently and intensely under excess labor supply, in comparison to excess labor demand. This trend is particularly pronounced among male participants. Additionally, workers display a decreased likelihood of accepting employment offers from more unfriendly managers and exert lower levels of effort when working under such managers, indicating that unfriendly leadership is costly. |
| Keywords: | leadership style, labor market competition, non-monetary incentives |
| JEL: | L20 M14 M55 |
| Date: | 2024–07–16 |
| URL: | https://d.repec.org/n?u=RePEc:bdp:dpaper:0042 |