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Combined Learning
Published in Hamidou Tembine, Distributed Strategic Learning for Wireless Engineers, 2018
The strategies {xj,t}t≥0 generated by these learning schemes are in the class of behavioral strategies τ˜ described above. The asymptotic behaviors of the CODIPAS-RL (A) are related to the multi-type replicator dynamics combined with the payoff dynamics. An important result in the field of evolutionary game dynamics is the folk theorem (evolutionary version). It states that, under the replicator dynamics of the expected two-player game, the following properties are satisfied:
Enhancing cyber-physical security in manufacturing through game-theoretic analysis
Published in Cyber-Physical Systems, 2018
Zach DeSmit, Aditya U. Kulkarni, Christian Wernz
Repeated games model cases where the players play the same game multiple times. Repeated games can either be finite, where the number of repetitions of the same game is finite, or infinite, where the players are assumed to repeat the same base game forever. For finitely repeated games, backward induction and SPNE is used to solve the game and find a player’s optimal strategies. For infinite games, one distinguishes between discounted and constant rewards. Constant reward games are those where rewards stay the same in each repetition of the game. In discounted games, future rewards are reduced by a discount factor There are two reasons for using a discount factor in infinitely repeated games. The first is due to mathematical tractability. The net expected future rewards for a player in repeated games with constant rewards often approach infinity, which makes the characterisation of an equilibrium strategy profile difficult. By multiplying all future rewards by an appropriate discount factor, mathematical tractability is ensured since the net future expected rewards of a player converge. The second reason is approximate a model of human behaviour [63]. Humans place more value on immediate rewards than those far in the future. Thus, by appropriately discounting future rewards, game-theorists can approximate human behaviour in infinitely repeated games. Infinitely repeated games are solved using strategies provided by the folk theorem [64,65].