### Game Theory: A Very Short Introduction

Ken Binmore, Oxford University Press 2007

**The name of the game****Chance****Time****Conventions****Reciprocity****Information****Auctions****Evolutionary biology****Bargaining and coalitions****Puzzles and paradoxes**

**Notable people:**John Von Neumann, David Hume, John Rawls, Emile Borel, John Nash, Immanuel Kant.

**Terms:**

Rationality - basing decisions in accordance to reason and logic.

Payoff - return on investment or bet; final outcome/conclusion.

Utility - assign a numerical value to each possible outcome to rate its usefulness in order to maximize.

Util - a unit on the utility scale used to measure and predict maximizing behaviour.

Risk neutral - assign the same number of utils to each extra unit quantity.

Risk adverse - assign fewer utils to each extra unit quantity.

Zero sum games - each player values each unit equally, thus a loss for one is a win for another.

Non-zero-sum game - This is when people make the hard effort to create a win-win solution(or at least, avoid a lose-lose) Without the non-zero-sum game, trust cannot evolve.

Nash equilibrium - all players are simultaneously making a best reply to the strategy choices of the others.

Prisoner's Dilemma - better situation but not best, while cooperating, but harsh punishment if both are selfish. Selfish and cooperate will end up with ok punishment, and very harsh respectively.

Mixed Nash equilibria - mixed strategy of pure strategy and randomization will keep the opposition guessing, making you less predictable while still keeping a positive chance of winning.

Non-zero-sum game - This is when people make the hard effort to create a win-win solution(or at least, avoid a lose-lose) Without the non-zero-sum game, trust cannot evolve.

Nash equilibrium - all players are simultaneously making a best reply to the strategy choices of the others.

Prisoner's Dilemma - better situation but not best, while cooperating, but harsh punishment if both are selfish. Selfish and cooperate will end up with ok punishment, and very harsh respectively.

Mixed Nash equilibria - mixed strategy of pure strategy and randomization will keep the opposition guessing, making you less predictable while still keeping a positive chance of winning.

**Briefs:**

A game is being played whenever human beings interact, game theory works only when people play rationally.

Animals with simple intellect act like automaton, irrational thought extinct from their genes.

Cooperation and conflict are two sides of the same coin.

Theory maxes a virtue of making no psychological assumptions at all.

We need the utility scale to measure the size of risk one is willing to take to get something. The options that will give the highest utility on average will be the best behavioural predictor.

Decide on a utility scale with discrete value 0 and 1, and assign util until the answer is switched from no to yes, thus the cost of the decision is worth say 75 utils. Each extra percentage point added to the indifference probability corresponds to one extra util.

The insurance industries existence confirms that it can be rational to gamble, if using calculated risks.

People tend to gamble only when they judge that the odd are in their favour.

Rational players reason their way to a solution, and people find their solution through evolutionary trail and error, knowing this we can predict what they will do.

All finite games have at least one equilibrium.

To make a vote count, we must follow through, else your vote doesn't count.

In mixed Nash equilibrium, the bigger the population the lower chances that anyone will help; or if one candidate is clearly inferior to another, a lack of voting because of the expected disapproval/lose, and expected approval/win for another candidate will bring out equilibrium for both parties.

Evolutionary game theory is the study of dynamic models, its application to evolutionary biology is important because humans enjoy feedback from all sources when learning how to behave in a new situation. Models of social and imitative learning converge more quickly and reliably on Nash equilibria than models of individuals learning by trial and error.

chapter 2 chance - minimax theorem

Rational players reason their way to a solution, and people find their solution through evolutionary trail and error, knowing this we can predict what they will do.

All finite games have at least one equilibrium.

To make a vote count, we must follow through, else your vote doesn't count.

In mixed Nash equilibrium, the bigger the population the lower chances that anyone will help; or if one candidate is clearly inferior to another, a lack of voting because of the expected disapproval/lose, and expected approval/win for another candidate will bring out equilibrium for both parties.

Evolutionary game theory is the study of dynamic models, its application to evolutionary biology is important because humans enjoy feedback from all sources when learning how to behave in a new situation. Models of social and imitative learning converge more quickly and reliably on Nash equilibria than models of individuals learning by trial and error.

*Personal Note:*chapter 2 chance - minimax theorem

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