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An example of a non-credible threat is demonstrated by Shaorong Sun & Na Sun in their book Management Game Theory. The example game, the market entry game, describes a situation in which an existing firm, firm 2, has a strong hold on the market and a new firm, firm 1, is considering entering. If firm 1 doesn’t enter, the payoff is (4,10).
Consider the sum of the two games. The claim that G 1 and G 2 have the same Sprague-Grundy value is equivalent to the claim that the sum of the two games has Sprague-Grundy value 0. In other words, we are to show that the sum G 1 + G 2 is a P-position. A player is guaranteed to win if they are the second player to move in G 1 + G 2.
Constant sum: A game is a constant sum game if the sum of the payoffs to every player are the same for every single set of strategies. In these games, one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.
This game is a common demonstration in game theory classes. It reveals the significant heterogeneity of behaviour. [11] It is unlikely that many people will play rationally according to the Nash equilibrium. This is because the game has no strictly dominant strategy, so it requires players to consider what others will do.
Determined game (or Strictly determined game) In game theory, a strictly determined game is a two-player zero-sum game that has at least one Nash equilibrium with both players using pure strategies. [2] [3] Dictator A player is a strong dictator if he can guarantee any outcome regardless of the other players.
Similarly, an auction is a game form that takes each bidder's price and maps them to both a winner and a set of payments by the bidders. Often, a game form is a set of rules or institutions designed to implement some normative goal (called a social choice function ), by motivating agents to act in a particular way through an appropriate choice ...
A third example of Parrondo's paradox is drawn from the field of gambling. Consider playing two games, Game A and Game B with the following rules. For convenience, define to be our capital at time t, immediately before we play a game. Winning a game earns us $1 and losing requires us to surrender $1.
In the game of Chomp strategy stealing shows that the first player has a winning strategy in any rectangular board (other than 1x1). In the game of Sylver coinage, strategy stealing has been used to show that the first player can win in certain positions called "enders". [4] In all of these examples the proof reveals nothing about the actual ...