Advances in Dynamic Games: Applications to Economics, by Alain Haurie, Shigeo Muto, Leon A. Petrosjan, T. E. S.

By Alain Haurie, Shigeo Muto, Leon A. Petrosjan, T. E. S. Raghavan

This publication, an outgrowth of the tenth foreign Symposium on Dynamic video games, provides present advancements of the speculation of dynamic video games and its functions. The textual content makes use of dynamic video game types to technique and clear up difficulties relating pursuit-evasion, advertising and marketing, finance, weather and environmental economics, source exploitation, in addition to auditing and tax evasions. It contains chapters on cooperative video games, that are more and more drawing dynamic methods to their classical recommendations.

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Extra info for Advances in Dynamic Games: Applications to Economics, Management Science, Engineering, and Environmental Management (Annals of the International Society of Dynamic Games)

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89–91]), which is provided by a matrix combined of two rows of the fundamental Cauchy matrix of system (1), one can pass to the equivalent game y˙ = D(t)u + E(t)v, t ∈ [t0 , T ], y ∈ R2 , u ∈ P, v ∈ Q, ϕ y1 (T ), y2 (T ) , (2) D(t) = Xi,j (T, t)B(t), E(t) = Xi,j (T, t)C(t). Here, the new phase variable y is two dimensional. The right-hand side of the dynamics does not contain the phase variable. The game interval, the constraints for controls, and the payoff function are the same as in the original game (1) (except that the payoff function now depends on components of the vector y).

Indeed, define the (ε, λ)-game to be a λ-discounted game, in which the stage payoff is rλε . The (ε, λ)-game differs from standard stochastic games in several respects. At each stage, the players choose mixed moves in ∆(A) and ∆(B) (and not actions in A and B). In addition, the stage payoff function depends on the discount factor being used. It can be checked that vλε coincides with the supinf of the (ε, λ)-game, when players are restricted to pure strategies. We conclude this section by offering a candidate for the max-min.

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