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Managerial Economics
Managerial Economics

... The relative cost of organising transaction through different forms of governance determined by: • Extent to which complete contracts are possible. Where contract refers to agreement between two parties which could be explicit or not. • Extent to which there is a threat of opportunism by parties in ...
Ch. 13: Game Theory
Ch. 13: Game Theory

Practice Problems II Answers
Practice Problems II Answers

... (If both drive a hard bargain, there’s no deal, so there’s zero change relative to the baseline. If both drive an easy bargain, Hector pays $700 for a $1000 gain, and Menelaus receives $700 for accepting a $400 loss, yielding net $300 each. If Hector drives an easy bargain and Menelaus a hard barga ...
PDF
PDF

CUR 412: Game Theory and its Applications Final
CUR 412: Game Theory and its Applications Final

... Q2. (24 pts) Consider two firms that play a Cournot duopoly game with inverse demand p = 100 − q and costs for each firm given by ci (qi ) = 10qi . Suppose that before the Cournot duopoly game, Firm 1 can choose to invest in cost reduction. If Firm 1 does, then it must pay a one-time cost of F , an ...
Emergence of cooperation and evolutionary stability in finite
Emergence of cooperation and evolutionary stability in finite

... ESS concept is neither necessary nor sufficient; for large populations, it is necessary but not sufficient (Fig 3). If we consider a game with many different strategies, then the two conditions must hold in paiwise comparison with every other strategy. Summing up, (i) in finite populations, natural ...
Prcpt04.pdf
Prcpt04.pdf

... But it is risky - if Row has misunderstood the game, or his hand trembles when he is making the choice, then Right may get Column a very bad payoff. So many Column players might choose the safer Left. This can be justified as a Nash equilibrium of a richer game where the possibility of Row making an ...
ppt - Stanford Security Lab
ppt - Stanford Security Lab

Game Theory and Strategic Behaviour
Game Theory and Strategic Behaviour

... Payoffs: The cost/benefit that each player gets from each possible outcome of the game (the prison sentences entered in each cell of the matrix) ...
Mixed Nash Equilibria 1 Normal Form Game 2 Pure Nash Equilibrium
Mixed Nash Equilibria 1 Normal Form Game 2 Pure Nash Equilibrium

... Proof of Theorem 2.11. Consider a finite normal form game. Without loss of generality let N = {1, . . . , n}, Si = {1, . . . , mi }. So the set of mixed states X can be considered a subset of P Rm with m = ni=1 mi . Exercise: Show that X is convex and compact. We will define a function f : X → X tha ...
Slide 1
Slide 1

breaking down poker ai
breaking down poker ai

PPT
PPT

notes
notes

MidtermSeanWayneRobinWayne
MidtermSeanWayneRobinWayne

Game Theory Basics - Cadmo
Game Theory Basics - Cadmo

An Approach to Bounded Rationality
An Approach to Bounded Rationality

gs2.aamas07 - Carnegie Mellon School of Computer Science
gs2.aamas07 - Carnegie Mellon School of Computer Science

... • Sequence form: More compact representation based on sequences of moves rather than pure strategies [Romanovskii 62, Koller & Megiddo 92, von Stengel 96] – Two-person zero-sum games can be solved in time polynomial in size of game tree – Doesn’t scale to Rhode Island Hold’em (3.1 billion nodes) or ...
Repeated Games - David Levine`s Economic and Game Theory Page
Repeated Games - David Levine`s Economic and Game Theory Page

Managerial Economics
Managerial Economics

Salop Model of Product Differentiation Consumers are located
Salop Model of Product Differentiation Consumers are located

... So far, we have assumed that players’ randomisations (when they play mixed strategies) are independent. In the 2×2 coordination games considered earlier, for instance, we can describe the mixed strategy equilibrium as follows: ...
Game Theory - Department of computing science
Game Theory - Department of computing science

... King-cobra males try to push each-other’s heads to the ground rather than biting Stags have roaring matches, walk parallel, and sometimes lock horns and push rather than trying to kill each-other When cats fight they scream more than they actually fight The more dangerous the species, the more ritua ...
Chapter 29
Chapter 29

... since we have actually seen some types of equilibria last time. • Game theory is concerned with the general analysis of strategic interaction. It can be used to study parlor games, political negotiation, and economic behaviors. ...
Repeated Games - UCSB Economics
Repeated Games - UCSB Economics

... of the game, it does not seem empirically plausible – why? Under the enter/accommodate equilibrium, the incumbent earns a payoff of 2x20 =40. But perhaps he can do better, for instance, suppose the incumbent chooses to fight the first 15 rivals and accommodate the last 5. If this strategy this is co ...
Simultaneous Move Games Lecture Four
Simultaneous Move Games Lecture Four

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Prisoner's dilemma

The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely ""rational"" individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it, ""prisoner's dilemma"" (Poundstone, 1992), presenting it as follows:Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is: If A and B each betray the other, each of them serves 2 years in prison If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa) If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get, and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with him, all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them to betray each other. The interesting part of this result is that pursuing individual reward logically leads both of the prisoners to betray, when they would get a better reward if they both kept silent. In reality, humans display a systematic bias towards cooperative behavior in this and similar games, much more so than predicted by simple models of ""rational"" self-interested action. A model based on a different kind of rationality, where people forecast how the game would be played if they formed coalitions and then they maximize their forecasts, has been shown to make better predictions of the rate of cooperation in this and similar games given only the payoffs of the game.An extended ""iterated"" version of the game also exists, where the classic game is played repeatedly between the same prisoners, and consequently, both prisoners continuously have an opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by backward induction) two classically rational players will betray each other repeatedly, for the same reasons as the single shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and Prisoner's Dilemma tournaments have been held to compete and test algorithms.The prisoner's dilemma game can be used as a model for many real world situations involving cooperative behaviour. In casual usage, the label ""prisoner's dilemma"" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it merely difficult or expensive, not necessarily impossible, to coordinate their activities to achieve cooperation.
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