66. The Dumping Game Mr. Jones and Mr. Smith own weekend homes on side by side plots of land in a remote area that has no routine garbage collection. They can contract to have their garbage picked up by a trucking firm, but it would cost either property owner $500 per year to arrange for the garbage pickup. Alternatively, Mr. Jones can sneak across the property line and dump his garbage on Mr. Smith's property, and similarly, Mr. Smith can dump his garbage on Mr. Jones's property.
67. The Game The two landowners will make their decisions simultaneously, so we will model it in normal form. Each landowner chooses between two strategies: pay for a garbage pickup or dump the garbage on the neighbor's property. But what are the payoffs in this game? The benefits the two landowners get from their weekend property are subjective benefits -- but …
68. The Payoffs We can estimate that the money value of a person's subjective enjoyment of his property – it is the smallest amount of rent that he would accept in return for giving up his own occupation of the property. We will say that each person values his experience at his weekend home at $5,000 per year if there is no dumping, but at $4,000 per year if there is.
72. “ Dump" is a “Dominant Strategy." Dominant Strategy -- Whenever one strategy yields a higher payoff than a second strategy, regardless which strategies the other players choose, the first strategy dominates the second. If one strategy dominates all other strategies (for a particular player in the game) it is said to be a dominant strategy (for that player.)
73. Dominant Strategy Equilibrium Dominant Strategy Equilibrium -- If, in a game, each player has a dominant strategy, and each player plays the dominant strategy, then that combination of (dominant) strategies and the corresponding payoffs are said to constitute the dominant strategy equilibrium for that game.
74. Noncooperative Equilibrium The dominant strategy equilibrium is a “noncooperative equilibrium.” In this case, though, Mr. Jones and Mr. Smith would probably prefer a “cooperative solution.”
75. Cooperative Equilibrium Cooperative solution -- the cooperative solution of a game is the list of strategies and payoffs that the participants would choose if they could commit themselves to an enforceable coordinated choice of strategies.
76. For Example, … Suppose, to continue the example, that Mr. Smith and Mr. Jones come together and negotiate a contract. The contract states that each of them will hire a truck, and that there will be no dumping. In fact, contracts of this kind among homeowners are quite common. They are called "covenants."
77. Social Dilemma 1. The Dumping Game, the Prisoner’s Dilemma, Advertising and Mobilization Games are examples of Social Dilemmas.
78. Social Dilemma 2. Social dilemma – A social dilemma is a game that has a dominant strategy equilibrium and the dominant strategy solution is different from the cooperative solution to the game.
79. Nash Equilibrium Nash Equilibrium— For any game in normal form: if there is a list of strategies, with one strategy per player, such that each strategy on the list is the best response to the other strategies on the list, that list of strategies is a Nash equilibrium.
82. How can we choose between two Nash equilibria? Schelling Point – If a game has two or more Nash equilibria, and some clue can lead the participants to believe that one equilibrium is more likely to be realized than the other, the more likely equilibrium is called a Schelling point.
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