But there would be two possible situations. First, they make agreement so that they can believe each other. In this case, if Player 1 believed Player 2’s announcement, the Player 1’s payoff would be like this.
Situation Expected payoffs
When Player 1 chose Rock Ep R =0· (0.4) +10· (0.3) -10· (0.3) 0
When Player 1 chose Scissors Ep S =-10(0.6) +0· (0.3) +10· (0.3) -1
When Player 1 chose Paper Ep P =10· (0.4)-10(0.3) +0· (0.3) 1
Therefore, Player 1 is going to put Paper as it draws the highest payoff of 1. But it is quite unrealistic assumption. In practical situation, Player 2’s announcement cannot be believed by rival because they are in zero-sum game so both players want to better off by deceiving the opponent. As a result, Player 1 has to
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Assume that slowing down the pitched fastball changes the payoff to the hitter in the “anticipate fastball/throw fastball” cell from 4 to 3. Explain carefully how you determine the answer here and show your work. Also explain why slowing the fastball can or cannot improve the pitcher’s expected payoff in the game.
PITCHER Throw curve(q) Throw fastball(1-q)
BATTER Anticipate curve(p) 2, -2 -1, 1 Anticipate fastball(1-p) -1, 1 3,- 3 Calculate p value: -3p+1=4p -3 (So, p*=4/7)
Pitcher’s expected payoff is
Ep C (P) + Ep F (P) = -2p +1(1-p) +1p-3(1-p) = -3p+1+4p -3 =p-2= -1.43
In the same way, if we calculate Batter’s expected payoff, it is 10/7
So, it shows that slowing the fastball cannot improve the pitcher’s expected payoff. [Ch.8]
1. Find Nash equilibrium in mixed strategies for the following game by using the method of best-response analysis. Draw a best-response diagram and show the equilibrium mixture on the diagram. Also indicate each player’s expected payoff in equilibrium.
1) Give probability to each option
COLUMN Left(q) Right(1-q)
ROW Up(p) 4, 0 -1, 2 Down(1-p) 1, 1 2, -1 2) Derive player’s expected pay-off
Row’s Expected Payoffs Column’s expected payoffs
EpU(R) = 4(q) - 1(1-q) = 5q-1 EpL(C) = 0(p) + 1(1-p) =
The game of baseball can be divided into three broad categories: hitting, pitching, and defense. No other facet of the game gets as much attention as hitting. For example, every year the MLB puts on a home run derby. No other part of the game draws as much attention. The traditional statistic that measure hitting ability is batting average (BA or AVG). To find a players batting averag...
Baseball is a fascinating sport that is exceptionally fun to play. This assignment is all about understanding the physics of a few key aspects of this sport. One might ask what physics could have to do with baseball? Like most sports baseball involves physical motion. Baseball encompasses all three planes of motion through throwing, hitting, and fielding. All of the classical laws of mechanics can be applied to understand the physics of this game.
...de that the reporter just wants to receive his reward of ten thousand dollars. However, they have made premature conclusions about Peter's covetousness because he has made the bill for just thirty-nine dollars and sixty cents. Such misunderstanding would never has happened if the protagonists did not hide the feelings and expressed their thoughts and assumptions to each other.
Ever since you were a child you have unknowingly used game theory. When your parents gave you the option to choose a candy bar, your brain started thinking of all the possibilities that depended on which candy you chose. You would think which one would taste better, make your feel better, and maybe be healthier for you. In the end, you would narrow your choices down to one piece of candy and eat it happily. Game theory is the use of theory to think through all of the positive and negative possibilities that could happen in a problem and try to maximize the positive. Game theory is not just one theory, throughout the years is has spread into six main games. These games are: zero sum games, non-zero sum games, simultaneous move games, sequential move games, one-shot games, and repeated games. Each of these games will be covered more in depth in this essay, with the exception of zero-sum games. Dalton will be writing about the zero-sum game in his essay.
Lewis, Michael. Moneyball: The Art of Winning an Unfair Game. New York City: W. W. Norton & Company, 2004. Print.
The Arizona Diamondbacks were one of the busiest teams this off-season trying to rebuild into a contender quickly. They bolstered their rotation with Zach Grinke and Shelby Miller those moves haven't necessarily worked out quite as well as Arizona envisioned to start the season, but both look to have gotten back on track. They also addressed the offensive side of the ball acquiring second baseman Jean Segura from the Milwaukee Brewers.
Bendix, Peter. (April 15, 2009). Ask The Professor: What is sabermetrics and why do baseball
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