dorsal/arxiv
View SchemaQuantization of the stag hunt game and the Nash equilibrilum
| Authors | Norihito Toyota |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307029 |
| URL | https://arxiv.org/abs/quant-ph/0307029 |
Abstract
In this paper I quantize the stag hunt game in the framework proposed by Marinatto and Weber which, is introduced to quantize the Battle of the Sexes game and gives a general quntization scheme of various game theories. Then I discuss the Nash equibilium solution in the cases of which starting strategies are taken in both non entangled state and entangled state and uncover the structure of Nash Equilibrium solutions and compare the case of the Battle of the Sexes game. Since the game has 4 parameters in the payoff matrix has rather rich structure than the Battle of the Sexes game with 3-parameters in the payoff matrix, the relations of the magnitude of these payoff values in Nash Equilibriums are much involuved. This structure is uncovered completly and it is found that the best strategy which give the maximal sum of the payoffs of both players strongly depends on the initial quntum state. As the bonus of the formulation the stag hunt game with four parameters we can discuss various types of symmetric games played by two players by using the latter formulation, i.e. Chicken game. As result some common properties are found between them and the stag hunt game. Lastly a little remark is made on Prisoner's Dillemma.
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"abstract": "In this paper I quantize the stag hunt game in the framework proposed by\nMarinatto and Weber which, is introduced to quantize the Battle of the Sexes\ngame and gives a general quntization scheme of various game theories. Then I\ndiscuss the Nash equibilium solution in the cases of which starting strategies\nare taken in both non entangled state and entangled state and uncover the\nstructure of Nash Equilibrium solutions and compare the case of the Battle of\nthe Sexes game. Since the game has 4 parameters in the payoff matrix has rather\nrich structure than the Battle of the Sexes game with 3-parameters in the\npayoff matrix, the relations of the magnitude of these payoff values in Nash\nEquilibriums are much involuved. This structure is uncovered completly and it\nis found that the best strategy which give the maximal sum of the payoffs of\nboth players strongly depends on the initial quntum state. As the bonus of the\nformulation the stag hunt game with four parameters we can discuss various\ntypes of symmetric games played by two players by using the latter formulation,\ni.e. Chicken game. As result some common properties are found between them and\nthe stag hunt game. Lastly a little remark is made on Prisoner\u0027s Dillemma.",
"arxiv_id": "quant-ph/0307029",
"authors": [
"Norihito Toyota"
],
"categories": [
"quant-ph"
],
"title": "Quantization of the stag hunt game and the Nash equilibrilum",
"url": "https://arxiv.org/abs/quant-ph/0307029"
},
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