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Published in David M. Levinson, Kevin J. Krizek, Metropolitan Transport and Land Use, 2018
David M. Levinson, Kevin J. Krizek
In game theory terms, you are playing zero-sum games with competitors and non-zero-sum games with complementors. A zero-sum game is so-called because the payoff of the game is fixed and split between the players, often with one player getting the entire payoff, and the other player losing an equivalent amount.31 In business terms, these are win–lose situations. An example is a football game: if my team wins, your team must lose. In a non-zero-sum game, on the other hand, there are gains from cooperation (either conscious or unconscious). In business terms, these are win–win situations. An example is gains from trade.
Engineering Decision Making
Published in Graeme Dandy, Trevor Daniell, Bernadette Foley, Robert Warner, Planning & Design of Engineering Systems, 2018
Graeme Dandy, Trevor Daniell, Bernadette Foley, Robert Warner
A strategic game involves two or more players who act rationally to promote their own interests. Provided there is no cooperation among the players, it is a non-cooperative game. The outcome of the game depends on the decisions of the players, but chance might also play a part in determining the outcome, which involves some players “winning’ and, usually, the other players “losing”. A zero-sum game is one in which the sum of the winnings for all players is equal to the sum of their losses.
Transportation decision models
Published in Zongzhi Li, Transportation Asset Management, 2018
As stated above, a two-person zero-sum game is a situation in which each player's gain or loss of utility is exactly balanced by the loss or gain of the utility of another player (Nash, 1953). If the total gains of the players are added up and the total losses are subtracted, they will sum to zero. Suppose the losses of the first player's utility is estimated as in Table 17.12. Let us see how the players play the two-person zero-sum game using the pure strategies.
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
Given the nature of iwoki, the characteristics and properties that must be taken into account when implementing the agents are as follows: First, it is a game with an opponent in which two agents are involved in a noncooperative way, since each agent looks after his/her own interests and they have no common objective. Thus, each player aims to get the highest score after the final point tally, which will make him/her the winner of the game. The rules of the game, the complete description of which is available at in the Appendix Section, are the same for the two players and known by both. The opponents will play their turn in a sequential and alternative way from the beginning to the end of the game. There are different strategies for the initial turn of the game, for the advance turns and for when the game is about to be over. The player who starts the game can also be the one who plays the last turn before the final point tally, which does not mean that he/she has more chances to win. Since everything a player wins for his/her own benefit is lost by the other player in the same proportion, and vice versa, it is categorized as a zero-sum game. In other words, what a player gains with respect to his opponent is the difference in the score obtained after the final point tally, which is accomplished by performing the best possible move in each turn. Finally, the game can be considered as deterministic or not, according to certain modifications necessary for the implementation of a particular agent, as it is specified in the Experimental Setup Section.
Nash equilibrium computation of two-network zero-sum games with event-triggered communication
Published in Journal of Control and Decision, 2021
Hongyun Xiong, Jiangxiong Han, Xiaohong Nian, Shiling Li
The zero-sum game satisfies , in particular, a two-person zero-sum game only has two players, and the sum of payoff functions of two players is 0. Two-network zero-sum game is a special multi-cluster game, in which two subnetworks are regarded as two players, the cost function of each subnetwork is the sum of the cost functions of all agents in the subnetwork. Besides, there is an important conclusion about the Nash equilibrium of zero-sum game: the Nash equilibrium set of two-person zero-sum game is the saddle point set of payoff function. Therefore, the problem of solving the Nash equilibrium of the zero-sum game is generally transformed into the problem of finding the saddle point of the payoff function.
A methodology for solving bimatrix games under 2-tuple linguistic environment
Published in International Journal of Systems Science: Operations & Logistics, 2023
The zero-sum games consider that whatever amount is won by one player, is the same amount lost by the other one. However, this is way too limiting for various games, like in politics or economics where both players may win or both may lose something. There are situations where the interests of both players may not be exactly the opposite. These types of situations bring about the concept of non-zero sum games, also called bimatrix games. In two-person non-zero sum games, both players have their individual payoff matrix. Both players aim to maximise their own individual payoff.