Game Theory

Game Theory
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Game Theory
In the Rock-Paper-Scissors game, optimal mixed-strategy is for every player to randomly select each option one-third of the time. However, supposing that when Rock beats Scissors, the winning player scores 2 points, not 1. Optimal play changes. The players Rock less, not more. Paper is played one-half of the time, and Rock and Scissors both drop to one-fourth. In a mixed-strategy, the game is played with probabilities 50%, 25%, or 25% respectively. Adding the aforementioned mixed-strategy – 50% Paper, 25% Rock, 25% Scissors – as an alternative for the player 1, then the anticipated payoffs for the first player against the second player’s pure strategies Paper, Rock, Scissors are 0, 0.25, –0.25 respectively.
PaperRockScissorsPaper01-1Rock-101Scissors1-1050-25-25 mix00.25-0.25
If player 1, Marylyn, plays the mixed strategy and Monroe plays Paper, then with 50 percent likelihood there would be a tie Paper vs. Paper, with 25 percent chance Monroe would win – her Paper against Marylyn’s Rock –, and with 25 percent chance Marylyn would show Scissors and win against Monroe’s Paper. As such, the anticipated payoff for Marylyn when she plays this mixed strategy against Monroe’s Paper will equal 50%·0 + 25%·(-1) + 25%·1 = 0. Therefore, the values within the 4th row are anticipated values of the matching values within the other rows and similar column, using the probabilities of the mix. The 2nd value within the 4th row is 0.25, and the 3rd one is -0.25. Although this new mixed strategy does not dominate the pure strategies, it might be attractive to a player who aims at the maximum strategy primarily because it promises a payoff of -0.25 in relation to 1- in the other 3 cases (Stevens, 2008). The strategies specified result in mixed-strategy equilibrium.
Considering the game of 2 people approaching one another on a sidewalk, each choosing right (R) or left (L), there are 3 Nash equilibria of the game. These are mixed strategy Nash equilibria and 2 pure equilibria. With pure strategy, the 2 people walking on the sidewalk will do the same thing all the time. In a mixed strategy, the 2 people will do dissimilar actions, and a probability would be assigned to each action (Stevens, 2008). The payoff from the mixed equilibrium is only half as good for either player of the...