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on Game Theory |
| By: | Zola, Maurizio Angelo |
| Abstract: | In a previous paper [1] the application of the dominance principle was proposed to fi nd the non-cooperative solution of the two by two general sum game with mixed strategies; in this way it was possible to choose the equilibrium point among the classical solutions avoiding the ambiguity due to their non-interchangeability, moreover the non-cooperative equilibrium point was determined by a new geometric approach based on the dominance principle. Starting from that result it is here below proposed the extension of the method to two persons general sum games with n by m moves. The algebraic two multi-linear forms of the expected payoffs of the two players are studied. From these expressions of the expected payoffs the derivatives are obtained and they are used to express the probabilities distribution on the moves after the two defi nitions as Nash and prudential strategies [1]. The application of the dominance principle allows to choose the equilibrium point between the two 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 non-cooperative solution of a two persons n by m 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. Some games from the sound literature are discussed in order to show the effectiveness of the presented procedure. |
| Keywords: | Dominance principle; General sum game; two persons n by m moves game |
| JEL: | C72 |
| Date: | 2024–10–07 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:122312 |
| By: | Putra, Diva Haqina |
| Abstract: | This paper analyzes the decision-making process between employees and employers regarding educational funding requests, using game theory. Employees, especially those with strong performance and alternative job offers, possess high bargaining power when negotiating for educational sponsorship as part of corporate social responsibility (CSR). The study models the interaction between employees and employers as a dynamic game with complete information, incorporating two subgames. In the first subgame, the employee decides whether to ask for funding, and the employer responds by accepting or rejecting the request. In the second subgame, the employee determines whether to stay or leave based on the employer's decision. The results show that the Nash Equilibrium suggests the optimal solution for both parties is for the employee to ask for funding, the employer to accept, and the employee to stay with the company. The analysis underscores the importance of investing in employee education for long-term organizational growth and retention. Keywords: Game theory, educational funding, employee bargaining power, corporate social responsibility (CSR), Nash equilibrium, employee retention. |
| Date: | 2024–09–17 |
| URL: | https://d.repec.org/n?u=RePEc:osf:osfxxx:e9j26 |
| By: | Dylan Laplace Mermoud |
| Abstract: | This paper studies the formation of the grand coalition of a cooperative game by investigating its possible internal dynamics. Each coalition is capable of forcing all players to reconsider the current state of the game when it does not provide sufficient payoff. Different coalitions may ask for contradictory evolutions, leading to the impossibility of the grand coalition forming. In this paper, we give a characterization of the impossibility, for a given state, of finding a new state dominating the previous one such that each aggrieved coalition has a satisfactory payoff. To do so, we develop new polyhedral tools related to a new family of polyhedra, appearing in numerous situations in cooperative game theory. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.05087 |
| By: | Martin Peitz; Susumu Sato |
| Abstract: | We propose a tractable model of asymmetric platform oligopoly with logit demand in which users from two distinct groups are subject to within-group and cross-group network effects and decide which platform to join. We characterize the equilibrium when platforms manage user access by setting participation fees for each user group. We explore the effects of platform entry, a change of incumbent platforms’ quality under free entry, and the degree of compatibility. We show how the analysis can be extended to partial user participation. |
| Keywords: | oligopoly theory, aggregative games, network effects, two-sided markets, two-sided single-homing, entry |
| JEL: | L13 L41 D43 |
| Date: | 2023–05 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_428v3 |
| By: | Margherita Comola (Université Paris-Saclay (RITM) and Paris School of Economics); Agnieszka Rusinowska (CES, CNRS - University Paris 1 Panthéon-Sorbonne and Paris School of Economics); Marie Claire Villeval (CNRS, Université Lumière Lyon 2, Université Jean-Monnet Saint-Etienne, emlyon business school, GATE, 69007, Lyon, France; IZA, Bonn, Germany) |
| Abstract: | We experimentally investigate how players with opposing views compete for influence through strategic targeting in networks. We varied the network structure, the relative influence of the opponent, and the heterogeneity of the nodes’initial opinions. Although most players adopted a best-response strategy based on their relative influence, we also observed behaviors deviating from this strategy, such as the tendency to target central nodes and avoid nodes targeted by the opponent. Targeting is also affected by affinity and opposition biases, the strength of which depends on the distribution of initial opinions. |
| Keywords: | Network; Influence; Targeting; Competition; Laboratory Experiment |
| JEL: | C91 D85 D91 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:gat:wpaper:2411 |
| By: | Squintani, Francesco (University of Warwick) |
| Abstract: | This paper brings together two major research streams in economic theory : information transmission in networks and strategic communication. The model embeds persuasion games of strategic disclosure by Milgrom (1981) into the communication network framework by Jackson and Wolinsky (1996). I find that the unique optimal network is a line in which players are ordered according to their bliss points. This ordered line is also pairwise-stable. This …nding stands in sharp contrast to previous results in network studies, that identify stars as the optimal and pairwise-stable networks when communication is non-strategic and subject to technological constraints. While stars are the most centralized minimally-connected networks, the line is the most decentralized one. These results may be especially relevant to political economy applications, such as networks of policymakers, interest groups, or judges |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1520 |
| By: | Li, Zhaolin (Erick); Liang, Guitian; Fu, Qi (Grace); Teo, Chung-Piaw |
| Abstract: | We study stationary base-stock policies for multiperiod dynamic inventory systems with a constant lead time and independently and identically distributed (iid) demands. When ambiguities in the underlying demand distribution arise, we derive the robust optimal base-stock level in closed forms using only the mean and variance of the iid demands. This simple solution performs exceptionally well in numerical experiments, and has important applications for several classes of problems in Operations Management. More important, we propose a new distribution-free method to derive robust solutions for multiperiod dynamic inventory systems. We formulate a zero-sum game in which the firm chooses a base-stock level to minimize its cost while Nature (which is the firm’s opponent) chooses an iid two-point distribution to maximize the firm’s time-average cost in the steady state. By characterizing the steady-state equilibrium, we demonstrate how lead time can affect the firm’s equilibrium strategy (i.e., the firm’s robust base-stock level), Nature’s equilibrium strategy (i.e., the firm’s most unfavorable distribution), and the value of the zero-sum game (i.e., the firm’s optimized worst-case time-average cost). With either backorders or lost sales, our numerical study shows that superior performance can be obtained using our robust base-stock policies, which mitigate the consequence of distribution mis-specification. |
| Keywords: | Inventory management, robust optimization, closed form, zero-sum game |
| Date: | 2023–03–15 |
| URL: | https://d.repec.org/n?u=RePEc:syb:wpbsba:2123/30211 |
| By: | Ying Chen (University of Nottingham Ningbo China); Tom Lane (Newcastle University); Stuart McDonald (University of Nottingham Ningbo China) |
| Abstract: | Using a laboratory experiment, we study the evolution of economic networks in the context of fragmented social identity. We create societies in which members can initiate and delete links to others, and then earn payoffs from a public goods game played within their network. We manipulate whether the society initially consists of segregated or integrated identity groups, and vary whether societal mobility is high or low. Results show in-group favouritism in network formation. The effects of original network structure are long-lasting, with initially segregated societies permanently exhibiting more homophilic networks than initially integrated ones. Moreover, allowing greater social mobility results in networks becoming less rather than more integrated. This occurs in part because eviction from networks is based on out-group hostility when societal mobility is high, and on punishing free riders when mobility across groups is low. |
| Keywords: | social identity; social network; in-group bias; homophily; laboratory experiments |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:not:notcdx:2024-07 |
| By: | Jan Knoepfle |
| Abstract: | This paper studies information transmission from multiple senders who compete for the attention of a decision maker. Each sender is partially informed about the state of the world and decides how to reveal her information over time to maximise attention. A decision maker wants to learn about the state but faces an attention cost. We derive a condition on the informational environment and the decision problem that guarantees that all information from the senders can be transmitted to the decision maker in equilibrium. A simple class of information processes implements full transmission across general environments. The attention each sender receives is proportional to the residual value of her information. In the case of conditionally iid-informed senders, in the limit as the number of senders grows large, the receiver learns the state exactly and immediately (at no attention cost). |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.18595 |
| By: | Marco Bornstein; Zora Che; Suhas Julapalli; Abdirisak Mohamed; Amrit Singh Bedi; Furong Huang |
| Abstract: | In an era of "moving fast and breaking things", regulators have moved slowly to pick up the safety, bias, and legal pieces left in the wake of broken Artificial Intelligence (AI) deployment. Since AI models, such as large language models, are able to push misinformation and stoke division within our society, it is imperative for regulators to employ a framework that mitigates these dangers and ensures user safety. While there is much-warranted discussion about how to address the safety, bias, and legal woes of state-of-the-art AI models, the number of rigorous and realistic mathematical frameworks to regulate AI safety is lacking. We take on this challenge, proposing an auction-based regulatory mechanism that provably incentivizes model-building agents (i) to deploy safer models and (ii) to participate in the regulation process. We provably guarantee, via derived Nash Equilibria, that each participating agent's best strategy is to submit a model safer than a prescribed minimum-safety threshold. Empirical results show that our regulatory auction boosts safety and participation rates by 20% and 15% respectively, outperforming simple regulatory frameworks that merely enforce minimum safety standards. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.01871 |
| By: | Salonia, Enrico Mattia |
| Abstract: | Revealed preference theory equates choices with preferences over the consequences these choices induce. Nevertheless, if a decision criterion prescribes an act for reasons unrelated to its consequences, the inference drawn regarding preferences can be misleading. I study the behaviour of non-consequentialist individuals who have preferences for universalisation. They choose the action that, in a counterfactual scenario where it is also chosen by everyone else, leads to their preferred consequences. I develop a model for individuals who value their choices in light of the counterfactual consequences they induce. Choices are interpreted as revealing a preference for counterfactual consequences. I impose axioms to single out the most prominent models of universalisation, compare them, highlight and arguably overcome their limitations. I propose a unifying model of universalisation inspired by the equal sacrifice principle. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:129835 |
| By: | Thomas R. Cook; Zach Modig; Nathan M. Palmer |
| Abstract: | Machine learning and artificial intelligence are often described as “black boxes.” Traditional linear regression is interpreted through its marginal relationships as captured by regression coefficients. We show that the same marginal relationship can be described rigorously for any machine learning model by calculating the slope of the partial dependence functions, which we call the partial marginal effect (PME). We prove that the PME of OLS is analytically equivalent to the OLS regression coefficient. Bootstrapping provides standard errors and confidence intervals around the point estimates of the PMEs. We apply the PME to a hedonic house pricing example and demonstrate that the PMEs of neural networks, support vector machines, random forests, and gradient boosting models reveal the non-linear relationships discovered by the machine learning models and allow direct comparison between those models and a traditional linear regression. Finally we extend PME to a Shapley value decomposition and explore how it can be used to further explain model outputs. |
| Keywords: | Machine learning; House prices; Statistical inference |
| JEL: | C14 C18 C15 C45 C52 |
| Date: | 2024–09–20 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2024-75 |