Download e-book for iPad: Subgame Consistent Economic Optimization: An Advanced by David W.K. Yeung

By David W.K. Yeung

ISBN-10: 0817682619

ISBN-13: 9780817682613

Various imperfections in present industry platforms hinder the unfastened industry from serving as a very effective allocation mechanism, yet optimization of monetary actions presents an efficient remedial degree. Cooperative optimization claims that socially optimum and separately rational suggestions to determination difficulties related to strategic motion through the years exist. to make sure that cooperation will final through the contract interval, although, the stringent situation of subgame consistency is required.

This textbook offers a research of subgame constant financial optimization, constructing game-theoretic optimization concepts to set up the basis for an efficient coverage menu to take on the suboptimal habit that the traditional industry mechanism fails to resolve.

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Extra info for Subgame Consistent Economic Optimization: An Advanced Cooperative Dynamic Game Analysis

Sample text

2. Economic agent i ∈ N seeks to maximize its objective T g i s, x(s), u1 (s), u2 (s), . . 1) t0 subject to the state dynamics x(s) ˙ = f s, x(s), u1 (s), u2 (s), . . , un (s) , x(t0 ) = x0 . 2) Now consider the case when the agents agree to act cooperatively. The agents agree to act according to an agreed-upon optimality principle. The agreement on how to act cooperatively and allocate cooperative payoff constitutes the solution optimality principle of a cooperative scheme. In particular, the solution optimality principle includes (i) an agreement on a set of cooperative strategies/controls and (ii) a mechanism to distribute the total payoff among agents.

The objectives of the duopolists are ∞ i πi G1 (s), G2 (s) − ui (s) exp −r(s − t0 ) ds, for i, j ∈ {1, 2}, t0 where πi is the constant unit margin of firm i. Chintagunta (1993), Feichtinger et al. (1994), Fershtman (1984), Sethi and Thompson (2000), and Tapiero (1979) considered games involving goodwill. 3 Market Equilibrium The outcome in the economic system (often known as market outcome when the system is driven by markets) is characterized by an equilibrium in which each participant is maximizing its objective given the other participants’ optimal choices of controls/strategies.

Gn . The dynamics of these experience stocks is ˙ i (s) = x i (s) − δGi (s), G Gi (t0 ) = Gi0 , for i ∈ N, where x i (s) is the market share of firm i. Firm i controls the ratio of its advertising expenditure to unit sales a i (s) and the ration of its promotion expense to unit sales bi (s). The market shares of firm i evolve according to n x˙ i (s) = x i (s)x j (s) f a i (s), x(s), Gi (s) j =1 − f a j (s), x(s), Gj (s) + g bi (s) − g bj (s) , x i (t0 ) = x0i , for i ∈ N, where x(s) = {x 1 (s), x 2 (s), .

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Subgame Consistent Economic Optimization: An Advanced Cooperative Dynamic Game Analysis by David W.K. Yeung


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