Download PDF by Takako Fujiwara-Greve (auth.): Non-Cooperative Game Theory

By Takako Fujiwara-Greve (auth.)

This is a textbook for college juniors, seniors, and graduate scholars majoring in economics, utilized arithmetic, and similar fields. each one bankruptcy is established in order that a middle suggestion of that bankruptcy is gifted with motivations, beneficial purposes are given, and similar complex subject matters are mentioned for destiny research. many useful routines at quite a few degrees are supplied on the finish of every bankruptcy. for this reason, this e-book is most fitted for readers who intend to review non-cooperative video game thought carefully for either theoretical reviews and applications.

Game thought includes non-cooperative video games and cooperative video games. This publication covers purely non-cooperative video games, that are significant instruments utilized in present economics and similar parts. Non-cooperative video game conception goals to supply a mathematical prediction of strategic offerings through selection makers (players) in events of conflicting curiosity. during the logical analyses of strategic offerings, we receive a greater realizing of social (economic, enterprise) difficulties and attainable treatments. The publication comprises many recognized video games resembling the prisoner’s quandary, poultry (hawk–dove) video game, coordination online game, centipede online game, and Cournot, Bertrand, and Stackelberg types in oligopoly. It additionally covers a few complicated frameworks reminiscent of repeated video games with non-simultaneous strikes, repeated video games with overlapping generations, worldwide video games, and voluntarily separable repeated prisoner’s trouble, in order that readers conversant in simple online game conception can extend their wisdom. The author’s personal learn is mirrored in subject matters reminiscent of formulations of knowledge and evolutionary balance, which makes this booklet unique.

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The sides (Heads or Tails) are the possible strategies each child may choose. The two players show one side of a coin simultaneously, and the game ends. The payoff of a player depends on the combination of the sides. If the sides are matched, child 1 wins and receives the coin from child 2. If the sides do not match, child 2 wins and receives the coin from child 1. 4. This game does not have a Nash equilibrium. For any strategy combination, there is a player (the loser) who can increase her/his payoff by changing the sides of the coin.

1 For any game G = ({1, 2, . . , n}, S1 , S2 , . . , Sn , u 1 , u 2 , . . , u n ), if a strategy combination s ∗ = (s1∗ , s2∗ , . . , sn∗ ) ∈ S is a Nash equilibrium, then it is not eliminated during the process of iterative elimination of strictly dominated strategies. Proof Suppose that a player’s strategy in the combination s ∗ is eliminated during the process of iterative elimination of strictly dominated strategies. There may be multiple such strategies, so let the first one that is eliminated in the process be si∗ .

There is a duopoly market, in which firm 1 and firm 2 are the only producers. Each firm chooses a price in {2, 3, 4} simultaneously. The payoff of a firm i ∈ {1, 2} is its sales, which is its price multiplied by its demand. The demand of a firm i ∈ {1, 2} is determined as follows. Let pi be firm i’s price and p j be the opponent’s. 6 − pi ) if pi = p j ⎩ 0 if pi > p j . 4. 7. (a) Find the set of strategy combinations that survive iterative elimination of strictly dominated strategies. (b) Assume that firms can choose a price from {1, 2, 3, 4}.

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