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Game Theory: Analyzing Strategic Interactions, Study Guides, Projects, Research of Law

An introduction to game theory, a mathematical framework used to analyze situations where the outcome of an action by one individual depends on the actions of others. It covers the two main categories of games: simultaneous and sequential, and discusses the impact of information and strategic interdependence on game outcomes. The document also explores the concept of payoffs and rational decision-making in strategic games, as well as the analysis of repeated games and cooperative vs non-cooperative scenarios.

Typology: Study Guides, Projects, Research

2023/2024

Available from 06/20/2024

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Game theory
Two main categories of games: simultaneous and sequential. Games can be one/repeated, co-
operative/non-cooperative. The amount of info in a game can affect its outcome.
The idea of game theory
Game theory is a technique used to analyse situations where for two or more people, the
outcome of an action by one of them depends on their action as well as those taken by the
other.
Strategic game – a scenario where for two or more people, their choice of action/behaviour
has an impact on others.
Strategic interdependence - strategies will depend on expectations about what the other party
is doing. Players need to take into account the possible actions of their counterparties when
they make their own decisions.
Describing strategic games
Games are defined in terms of their rules. The rules incorporate information about players,
their knowledge of the game, possible moves/actions and payoffs. A payoff that represents
more utility will be preferred to one that represents less.
Players acting rationally choose strategies to maximise their payoffs. But because of the
interdependence, a player’s best strategy will depend on what they think the other players are
likely to do.
Simultaneous games
Players make moves at the same time. Players therefore need to formulate strategies on the
basis of what they think the other players will do.
Pure conflict/zero sum games – one player wins and the other loses (one player’s gain is the
other’s loss). (GoC)
Mixed motive games – games which have some scope for mutual gain through co-
ordination/assurance. There are therefore mutually beneficial/harmful outcomes so that there
are shared objectives. (PD, Stag-hunt)
Mixed strategy – a mix of pure strategies determined by a randomisation procedure e.g.
throwing a dice.
Sequential games
Players make moves in some sort of order e.g. one player moves first then the other player
sees this and responds e.g. Chess.
The best way to analyse these games is through game tress.
Repetition
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Game theory Two main categories of games: simultaneous and sequential. Games can be one/repeated, co- operative/non-cooperative. The amount of info in a game can affect its outcome. The idea of game theory Game theory is a technique used to analyse situations where for two or more people, the outcome of an action by one of them depends on their action as well as those taken by the other. Strategic game – a scenario where for two or more people, their choice of action/behaviour has an impact on others. Strategic interdependence - strategies will depend on expectations about what the other party is doing. Players need to take into account the possible actions of their counterparties when they make their own decisions. Describing strategic games Games are defined in terms of their rules. The rules incorporate information about players, their knowledge of the game, possible moves/actions and payoffs. A payoff that represents more utility will be preferred to one that represents less. Players acting rationally choose strategies to maximise their payoffs. But because of the interdependence, a player’s best strategy will depend on what they think the other players are likely to do. Simultaneous games Players make moves at the same time. Players therefore need to formulate strategies on the basis of what they think the other players will do. Pure conflict/zero sum games – one player wins and the other loses (one player’s gain is the other’s loss). (GoC) Mixed motive games – games which have some scope for mutual gain through co- ordination/assurance. There are therefore mutually beneficial/harmful outcomes so that there are shared objectives. (PD, Stag-hunt) Mixed strategy – a mix of pure strategies determined by a randomisation procedure e.g. throwing a dice. Sequential games Players make moves in some sort of order e.g. one player moves first then the other player sees this and responds e.g. Chess. The best way to analyse these games is through game tress. Repetition

One shot/unrepeated games – games played once by the same players Repeated games – players by the same players more than once Repeated games need to set out moves they plan to make at each repetition called meta- strategies. Cooperative v non-cooperative games Cooperative – players are allowed to communicate and agreement about how to play the game are enforceable. Because the agreements are enforceable, the players have an incentive to agree on mutually beneficial outcomes. Non-cooperative – players act only in their own self-interest. Axelrod – Effective choice in the Prisoner’s dilemma Distinguishing feature of the PD is that in the short run, neither side can benefit itself with a selfish choice enough to make up for the harm done to it from a selfish choice by the other. If both parties cooperate, they both do fairly well. The high payoff for defecting gives both sides an incentive to defect. If both defect, both do poorly. PD embodies the tension between individual rationality (incentive to be selfish) and group rationality (higher payoff for mutual cooperation over mutual defection). The fact that games are repeated, and players often have ongoing relationships and an important future means there needs to be effective choices made. Minimize echo effects (where you’re punished for punishing another player and it continues like this). Be ‘nice’ – never be the first to defect, at least until the last few moves. ‘Forgive’ – punishing each defection by the other side only once. Forgiveness prevents amplification of echoes.