New PDF release: Games, Theory and Applications (Dover Books on Mathematics)

By L. C. Thomas

ISBN-10: 0486432378

ISBN-13: 9780486432373

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Extra info for Games, Theory and Applications (Dover Books on Mathematics)

Example 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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Games, Theory and Applications (Dover Books on Mathematics) by L. C. Thomas


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