Introduction to game theory

By Karl Tuyls, Ann Nowé. Wiley Encyclopedia of Computer Science and Engineering, 2003

1,647 citations recorded by the source corpus.

The basic ideas of game theory were originated from the problems of maximum and minimum given by J. von Neumann in 1928. Later, wars accelerated the study of game theory, there are many developments that contributed to the advancement of game theory, many problems of optimum appeared in economic development process. Scientists applied mathematic methods to studying game theory to make the theory more profound and perfect. The axiomatic structure of game theory was nearly complete in 1944. The path of the development of game theory started from finite to infinite, from two players to many players, from expressing gains with quantity to showing the ending of game theory with abstract result, and from certainty problems to random problems. Thus development of game theory is closely related to the economic development. In recent years, the research on the non-differentiability of Shapley value posed by Belgian Mertens is one of the advanced studies in game theory.

Subfields: Artificial Intelligence, Management Science and Operations Research, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/ef33b0edda2ed1a451e8f40ca641cc73d1c7f7e3

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Citations in the corpus

Interference Management for Cellular-Connected UAVs: A Deep Reinforcement Learning Approach (2018, methodology): “To show that our proposed scheme guarantees convergence to an SPNE, we use the following lemma from [28].”
Price-Based Spectrum Management in Cognitive Radio Networks (2007, background): “However, this NE is generally not Pareto optimal [20] and may be quite inefficient in term of sum-rate [4].”
Energy Sharing Management for Microgrids With PV Prosumers: A Stackelberg Game Approach (2017, methodology): “We can find optimized prices pb and p ∗ s by using the backward inference method [27].”
Computer poker: A review (2011, background): “In general, a set of strategies are said to be in equilibrium if the result of one player diverging from their equilibrium strategy (while all other players stick to their current strategy) results in a negative impact on the expected value for the player who modified their strategy [59].”
Evolutionary game theory: Theoretical concepts and applications to microbial communities (2010, background): “Classical Game Theory [2] describes the behavior of rational players.”
Reward Tampering Problems and Solutions in Reinforcement Learning: A Causal Influence Diagram Perspective (2019, methodology): “For example, in the rocks and diamonds environment, the agent may know that asking the fool will yield feedback Drock = Ddiamond = 1 regardless of Θ R ∗ , and therefore refrain from updating its estimate of Θ ∗ after visiting the fool. Furthermore, the only directed paths from D1:m to reward nodes p”
Deep Reinforcement Learning for User Association and Resource Allocation in Heterogeneous Cellular Networks (2019, background): “we can derive that an SPNE exists in each finite game with perfect memory [38].”
Game theory approach to the analysis of inter-plant water integration in an eco-industrial park (2009, background): “In any non-cooperative game, Nash equilibrium is a solution from which no player can unilaterally deviate in order to improve his/her payoff [44–47].”
Multi-player non-zero-sum games: Online adaptive learning solution of coupled Hamilton-Jacobi equations (2011, background): “Game theory (Tijs, 2003) has been very successful in modeling strategic behavior, where the outcome for each player depends on the actions of himself and all the other players.”
Dynamics of Multiple-Seller and Multiple-Buyer Spectrum Trading in Cognitive Radio Networks: A Game-Theoretic Modeling Approach (2009, background): “The Nash equilibrium [28] is a desired solution since it ensures that none of the players in the game will deviate from the equilibrium [29].”
Competitive Pricing for Spectrum Sharing in Cognitive Radio Networks: Dynamic Game, Inefficiency of Nash Equilibrium, and Collusion (2008, background): “By definition, the Nash equilibrium of a game is a strategy profile (list of strategies, one for each player) with the property that no player can increase his payoff by choosing a different action, given other players’ actions [20].”
Dynamics of Network Selection in Heterogeneous Wireless Networks: An Evolutionary Game Approach (2009, background): “For the competition on network selection, the Nash equilibrium gives a strategy profile (list of strategies, one for each player) with the property that no player can increase his payoff by choosing a different action, given other players’ actions [22].”
Energy-Efficient Resource Allocation for Heterogeneous Cognitive Radio Networks with Femtocells (2012, background): “Hence, the Nash equilibrium of a game is a strategy equilibrium that no primary network can increase its revenue by choosing a different strategy, given other players’ strategy [32].”
The explanation paradox (2012, methodology): “However, that was not too damaging for the minimum differentiation principle because there are a variety of settings in which that result holds, including a game theoretic set-up without price competition (eg, Osborne 2004 , sec.”
Leader-Based Optimal Coordination Control for the Consensus Problem of Multiagent Differential Games via Fuzzy Adaptive Dynamic Programming (2015, methodology): “Game theory [17] studies strategic decision making problems.”