Ch3 - Game Theory, Textbook & Summary notes summarised. PDF

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Chapter 3 of Microeconomics textbook and lecture notes. Summarised. ...

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Chapter 3 Game Theory Social Dilemmas As discussed in chapter 1, we discussed how an activity is worth doing if the benefits exceed the costs. However, there are many external benefits and costs that fall on other people other than those directly affected by the activity. An example of this is someone lighting a cigarette in a restaurant, where people sitting nearby will be affected.

The image is described as a “payoff matrix”. It shows the payoff 2 individuals will get when they both make a decision in correspondence to the others decision.

Dominant strategy is the strategy in the game that produces better results no matter what the other person choses. E.g. Jill’s dominant strategy is to always sell 40 Gallons. This is because her payoffs are higher doing that when Jack sells 30 OR 40 gallons himself. ($1,600 > $1,500 & $2,000 > $1,800) However, notice how even if both of their dominant strategies is to sell 40 gallons, they would both be worse off ($1600) if they did that rather than both selling 30 gallons ($1800).

This explains how the optimal individual decision does not lead to the best collective outcome all the time. Furthermore, this is not considered Pareto Efficient (A situation where one person cannot be better off without harming someone else.) Because of the tensions between individual incentives and Pareto

efficiency this type of game is known as a social dilemma. The most obvious social dilemma being the Prisoners Dilemma. Commitment problems Social Dilemmas as discussed before are an example of a broader class of problems known as commitment problems The common feature of these problems is that people would do better if they could collectively commit themselves to cooperate and go against their material interests. Generally, players in social dilemmas would do better to cooperate despite the incentive to defect. Repeated games Failing to cooperate in social dilemmas can be costly. So people who cooperate would probably like a way to penalize those who defect. Now whilst this is hard to do when meeting a limited amount of times or even once, if the game is repeated then it becomes relatively easy to do. “Tit for Tat” is the strategy to do so. It involves cooperating when interacting with someone the first time and then after that you do whatever they did previously. For example, if they defect the first time then you will defect the second time. If two “tit for tat” players interact together over a long period of time, then the result will be cooperation in every interaction. It is considered a “tough” strategy as people who follow it can easily punish defectors in the next interaction, furthermore it is considered a “forgiving” strategy as the player is willing to cooperate with a former defector once she shows evidence of willingness to cooperate. However, another requirement for this to work is that there is no known end to the interactions as this can make people tempted to defect on the final play etc.

Nash equilibrium A combination of strategies where each player is doing the best they can, given the others choice is called a Nash Equilibrium. If a player would want to move from the box they are currently in (afters the others choice) then they aren’t in Nash equilibria. Referring to the “Jack & Jill Oligopoly game” let’s consider the top left box. Jill would not want to move down and Jack would not want to move to the right. Therefore, this is Nash equilibria. However, say the bottom left corner, Jill would

want to move if Jack produced 40 gallons but Jack wouldn’t move if Jill produced 30 gallons. An example from Tutorial W3 asks the same thing.

The top right and, bottom left is both considered “Nash Equilibria” as neither firm would want to move. Remember they can only change between their own 2 choices, they can’t want to move to a corner that requires changing the others answer, in other words the oppositions answer is set. Coordination games A coordination game is where the two individuals want to choose the same option, such as both driving on the left hand side of the road. A Coordination failure occurs when the two individuals chose different strategies, a miscoordination is where both chose the same option, but a more inefficient one then there was available. The difference between a coordination game and the prisoner’s dilemma is that in a coordination game, the issue is to choose a strategy that is coherent with that chosen by the other players. In a prisoner’s dilemma game, the issue is that the outcome that is best for all players cannot reliably be achieved because the dominant strategy for each player is one that leads to another, worse outcome....