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Electricity restructuring and deregulation
Published in Peter M. Schwarz, Energy Economics, 2023
Notice that had they stuck to a high-priced agreement, they would have each done better. Such a game is a Prisoner’s Dilemma, a game in which the Nash equilibrium does not lead to the best outcome for the players. To avoid the Prisoner’s Dilemma, the two players could find a way to convert a noncooperative game into a cooperative game. If they know they will play this game repeatedly, the payoff for preventing the Prisoner’s Dilemma is greater. They may be able to build up trust that if they agree to a high price, they will stick to the agreement. If they cannot cooperate, they may have to resort to threats of retaliation if a firm violates the agreement. In order for a threat to work, it must be credible; that is, the potential violator believes that the other player will be better off if it carries out the threat than if it does not.
Using Decision Theory and Value Alignment to Integrate Analogue and Digital AI
Published in Maurizio Tinnirello, The Global Politics of Artificial Intelligence, 2022
This leads us to an important mathematical result that affects that possibility. Andrew Critch generalised Löb's theorem to proof systems with bounded computational resources.26 With this result, Critch was able to demonstrate that if the algorithm players in classic non-cooperative games (e.g. prisoners' dilemma) are able to read each other's source codes, then such expected utility-maximising players can achieve mutual cooperation. For example, in the two-player prisoners' dilemma, when expected utility-maximising players know each other's source codes, players will both cooperate or both defect, but never be in a situation where one cooperates and one defects. This is a superior equilibrium for both players compared to the classic Nash equilibrium, where both players defect.
Data Analysis
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
Raymond R. Hill, Darryl K. Ahner
If SNE≠0; then there exists an action profile for each player such that if both players choose their respective action profile, there is no incentive to deviate from this action profile. Let |SNE| be the cardinality (the number of elements) of the set SNE. If |SNE|>1 then multiple Nash equilibria exist; however, Nash equilibria need not be equally preferable. Depending on the player utility function or payoff values, an action profile that is also a Nash equilibrium could be better than another action profile that is also a Nash equilibrium. Further analysis is needed after SNE has been obtained to decide on which action profile to focus.
When communicative AIs are cooperative actors: a prisoner’s dilemma experiment on human–communicative artificial intelligence cooperation
Published in Behaviour & Information Technology, 2022
The present study employed a two-player version of prisoner’s dilemma experiment to examine the possibility of human–communicative AI cooperation. Prisoner’s dilemma is a social dilemma which can be used as a framework for the study of mutual cooperation (Axelrod and Hamilton 1981; Rapoport and Chammah 1965), and has been applied in various fields including biology (Axelrod and Hamilton 1981), economics (Kreps et al. 1982), political science (Axelrod 1980a, 1980b), psychology (Balliet, Mulder, and Van Lange 2011; Balliet and Van Lange 2013), and sociology (Macy 1996). In short, two individuals either cooperate or defect in the game. The dilemma is that both get worse when both of them defect, rather than both cooperate. Mutual cooperation yields a higher payoff than mutual defection. However, mutual defection is a Nash equilibrium. It is because if one cooperates and the other one defects, this situation yields a lower payoff for the cooperative side. Prisoner’s dilemma experiment has been successfully adopted to investigate human–computer agent cooperation (Baker and Rachlin 2002; Kiesler, Sproull, and Waters 1996; Miwa and Terai 2012; Parise et al. 1999).
Performance Study of Minimax and Reinforcement Learning Agents Playing the Turn-based Game Iwoki
Published in Applied Artificial Intelligence, 2021
Santiago Videgaín, Pablo García Sánchez
Von Newman and Morgenstern (Von Neumann and Morgenstern 2007) define the concept of zero-sum games with an opponent, in which everything a player manages to win corresponds to what his/her opponent loses. In other words, the sum of what one wins and the other loses is zero. An example of a zero-sum game is an individual tennis match, where each player’s point is detrimental to the opponent. However, in a doubles tennis match, the points scored by a partner is also used by the other. This case is an example of a non-zero-sum play. John Forbes Nash adds a new concept for non-zero-sum cases: the so-called Nash Equilibrium, a situation in which none of the players is interested in modifying their individual strategy so as not to be disadvantaged, knowing their opponents’ one (Daskalakis, Goldberg, and Papadimitriou 2009).
Cybersecurity investments in a two-echelon supply chain with third-party risk propagation
Published in International Journal of Production Research, 2021
Nash equilibrium is the solution of a non-cooperative game with two or more players, where no player can benefit by changing his or her own strategy while the other players keep theirs unchanged. To ensure the existence of the Nash equilibrium, the slope of by (8) should be greater than the slope of by (6) to ensure the two reaction curves (Glicksberg 1956; Wu et al. 2015). Thus, the slope of the reaction curve at the equilibrium point should satisfy the following condition: Simplifying (11), the equilibrium condition is obtained As a sufficient condition, (12) guarantees that the Nash equilibrium of cybersecurity investment in this supply chain can be achieved.