Różnice między wybraną wersją a wersją aktualną.
| Both sides previous revision Poprzednia wersja Nowa wersja | Poprzednia wersja | ||
|
pl:dydaktyka:dss:projects:equilibrium:start [2018/01/28 13:21] mjedrze [Main topic - Equilibrium:] |
pl:dydaktyka:dss:projects:equilibrium:start [2019/06/27 15:50] (aktualna) |
||
|---|---|---|---|
| Linia 1: | Linia 1: | ||
| - | ==== Main Page ==== | ||
| ==== Game Theory - Nash Equilibrium ==== | ==== Game Theory - Nash Equilibrium ==== | ||
| Linia 15: | Linia 14: | ||
| 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. | ||
| Linia 43: | Linia 42: | ||
| - **game tree** - it is build from players moves, leafs hold payoffs values | - **game tree** - it is build from players moves, leafs hold payoffs values | ||
| - | TODO DODAĆ OBRAZEK | + | {{:pl:dydaktyka:dss:projects:equilibrium:gametree.png?nolink&600|}} |
| Linia 81: | Linia 80: | ||
| === Equilibrium === | === Equilibrium === | ||
| + | |||
| + | {{: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. | ||
| Linia 94: | Linia 95: | ||
| 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 110: | 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|}} | ||
| === Others equilibriums: === | === Others equilibriums: === | ||
| Linia 222: | Linia 223: | ||
| Let's see how we can work with Game Theory Explorer: | Let's see how we can work with Game Theory Explorer: | ||
| - | 1. Go to http://gte.csc.liv.ac.uk/gte/builder/ and activate flash | + | Ordered List Item |
| - | 2. Click Strategic Form and then "Click to edit", | + | - Go to http://gte.csc.liv.ac.uk/gte/builder/ and activate flash |
| + | - Click Strategic Form and then "Click to edit", | ||
| - | 3. Now we are ready to model a game, write payoffs and strategy names for each player, then click "Confirm changes and align payoffs" | + | {{:pl:dydaktyka:dss:projects:equilibrium:punkt2.png?nolink|}} |
| + | |||
| + | - Now we are ready to model a game, write payoffs and strategy names for each player, then click "Confirm changes and align payoffs" | ||
| - | TODO zdjęcia | ||
| - | |||
| - | |||
| - | |||
| - | |||
| - | |||
| - | |||
| - | |||
| - | |||
| + | {{:pl:dydaktyka:dss:projects:equilibrium:punkt3.png?nolink|}} | ||
| - | 4. You can also see how you game looks in tree form and matrix layout. | + | - You can also see how you game looks in tree form and matrix layout. |
| + | {{:pl:dydaktyka:dss:projects:equilibrium:punkt4a.png?nolink|}} | ||
| + | {{:pl:dydaktyka:dss:projects:equilibrium:punkt4b.png?nolink|}} | ||
| - | 5. Now you can use Game Explorer to run your model and find Equilibrium. | + | - Now you can use Game Explorer to run your model and find Equilibrium. |
| + | {{:pl:dydaktyka:dss:projects:equilibrium:punkt5.png?nolink|}} | ||
| Linia 257: | Linia 255: | ||
| **Exercise 3:** | **Exercise 3:** | ||
| 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&600|}} | ||
| **Exercise 4:** | **Exercise 4:** | ||
| Linia 265: | Linia 265: | ||
| If you want to see how already mentioned games look like in game theory explorer, you can use already prepared files: | If you want to see how already mentioned games look like in game theory explorer, you can use already prepared files: | ||
| - | - exam.xml | + | |
| - | - PRISON DILEMMA.xml | + | {{:pl:dydaktyka:dss:projects:equilibrium:open.png?nolink&400|}} |
| - | - RockPaperScissors.xml | + | |
| - | - RockPaperScissorsLizardSpock.xml | + | {{ :pl:dydaktyka:dss:projects:equilibrium:exam.xml |}} |
| - | - BattleOfSexes1.xml | + | |
| - | - BattleOfSexes2.xml | + | {{ :pl:dydaktyka:dss:projects:equilibrium:battleofsexes1.xml |}} |
| + | |||
| + | {{ :pl:dydaktyka:dss:projects:equilibrium:battleofsexes2.xml |}} | ||
| + | |||
| + | {{ :pl:dydaktyka:dss:projects:equilibrium:prison_dilemma.xml |}} | ||
| + | |||
| + | {{ :pl:dydaktyka:dss:projects:equilibrium:rockpaperscissors.xml |}} | ||
| + | |||
| + | {{ :pl:dydaktyka:dss:projects:equilibrium:rockpaperscissorslizardspock.xml |}} | ||
| + | |||
| + | |||
