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pl:dydaktyka:dss:projects:equilibrium:start [2018/01/28 13:53] mjedrze [DESCRIPTION OF PRISON DILEMMA] |
pl:dydaktyka:dss:projects:equilibrium:start [2019/06/27 15:50] (aktualna) |
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| - | ==== Main Page ==== | ||
| ==== Game Theory - Nash Equilibrium ==== | ==== Game Theory - Nash Equilibrium ==== | ||
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| A strategy defines a set of moves or actions a player will follow in a given game. A strategy must be complete, defining an action in every contingency, including those that may not be attainable in equilibrium. For example, a strategy for the game of checkers would define a player's move at every possible position attainable during a game. Such moves may be random, in the case of mixed strategies. | A strategy defines a set of moves or actions a player will follow in a given game. A strategy must be complete, defining an action in every contingency, including those that may not be attainable in equilibrium. For example, a strategy for the game of checkers would define a player's move at every possible position attainable during a game. Such moves may be random, in the case of mixed strategies. | ||
| - | strategy=/=move | + | **strategy=/=move** |
| The strategy concept is sometimes (wrongly) confused with that of a move. A move is an action taken by a player at some point during the play of a game (e.g., in chess, moving white's Bishop a2 to b3). A strategy on the other hand is a complete algorithm for playing the game, telling a player what to do for every possible situation throughout the game. | The strategy concept is sometimes (wrongly) confused with that of a move. A move is an action taken by a player at some point during the play of a game (e.g., in chess, moving white's Bishop a2 to b3). A strategy on the other hand is a complete algorithm for playing the game, telling a player what to do for every possible situation throughout the game. | ||
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| - **game tree** - it is build from players moves, leafs hold payoffs values | - **game tree** - it is build from players moves, leafs hold payoffs values | ||
| - | {{:pl:dydaktyka:dss:projects:equilibrium:gametree.png?nolink&400|}} | + | {{:pl:dydaktyka:dss:projects:equilibrium:gametree.png?nolink&600|}} |
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| === Equilibrium === | === Equilibrium === | ||
| - | {{:pl:dydaktyka:dss:projects:equilibrium:xkcd.png?nolink&400|}} | + | {{:pl:dydaktyka:dss:projects:equilibrium:xkcd.png?nolink|}} |
| An equilibrium, (or Nash equilibrium, named after John Nash) is a set of strategies, one for each player, such that no player has incentive to unilaterally change his action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with his current strategy. For games in which players randomize (mixed strategies), the expected or average payoff must be at least as large as that obtainable by any other strategy. | An equilibrium, (or Nash equilibrium, named after John Nash) is a set of strategies, one for each player, such that no player has incentive to unilaterally change his action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with his current strategy. For games in which players randomize (mixed strategies), the expected or average payoff must be at least as large as that obtainable by any other strategy. | ||
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| An equilibrium refinement provides a way of selecting one or a few equilibriums from among many in a game. Many games may contain several Nash equilibriums, and thus offer no clear prediction about the likely outcome. Each refinement attempts to define some equilibriums as "more likely," "more rational" or "more robust" to deviations by players than others. For example, if one equilibrium Pareto dominates another (results in all players earning more ), then it may be viewed as more likely to be chosen by the players. | An equilibrium refinement provides a way of selecting one or a few equilibriums from among many in a game. Many games may contain several Nash equilibriums, and thus offer no clear prediction about the likely outcome. Each refinement attempts to define some equilibriums as "more likely," "more rational" or "more robust" to deviations by players than others. For example, if one equilibrium Pareto dominates another (results in all players earning more ), then it may be viewed as more likely to be chosen by the players. | ||
| + | <fc #fffff></fc> | ||
| **QUESTION 1:** What is the equilibrium of the below game? | **QUESTION 1:** What is the equilibrium of the below game? | ||
| | | ^ Player 2 || | | | ^ Player 2 || | ||
| - | | | | X | Y | | + | | | | X | Y | |
| - | ^ Player 1 | A | 10 , 10 | 15 , 5 | | + | ^ Player 1 | A <fc #ffffff>spja</fc> | 10 , 10 | 15 , 5 | |
| - | | ::: | B | 5 , 15 | 12 , 12 | | + | | ::: | B <fc #ffffff>scja</fc> | 5 , 15 | 12 , 12 | |
| Linia 112: | Linia 111: | ||
| Consider following situation: there are two convenient stores right next to your house, your Nash Strategy when buying milk in the morning would be to go to the cheapest store, given each store’s price. And similarly, the Nash Strategy for the storekeeper would be to price their milk just below their competitor in order to attract you, given their competitor’s price and your strategy of going for the cheapest store. | Consider following situation: there are two convenient stores right next to your house, your Nash Strategy when buying milk in the morning would be to go to the cheapest store, given each store’s price. And similarly, the Nash Strategy for the storekeeper would be to price their milk just below their competitor in order to attract you, given their competitor’s price and your strategy of going for the cheapest store. | ||
| - | {{:pl:dydaktyka:dss:projects:equilibrium:fun.png?nolink&400|}} | + | {{:pl:dydaktyka:dss:projects:equilibrium:fun.png?nolink|}} |
| === Others equilibriums: === | === Others equilibriums: === | ||
| Linia 257: | Linia 256: | ||
| Create model of rock, paper, scissors , lizard, Spock game for two players and check if it have equilibrium. | Create model of rock, paper, scissors , lizard, Spock game for two players and check if it have equilibrium. | ||
| - | {{:pl:dydaktyka:dss:projects:equilibrium:rockpaperscissorslizardspock.jpg?nolink&400|}} | + | |
| + | {{:pl:dydaktyka:dss:projects:equilibrium:rockpaperscissorslizardspock.jpg?nolink&600|}} | ||
| **Exercise 4:** | **Exercise 4:** | ||
