Welcome to Module 3 on Simultaneous Games
Going back to the 6 questions that define the many types of games, let’s make one small change .
In this module, we assume that the players in the game move “simultaneously”, meaning that at the times and situations that decisions are made no player can see/observe anything about what other players are doing. But , while unable to directly observe th behaviour of others, rational players can think – i.e. about what the other players could do, what the other players are thinking about what …other players will do…and think. (Remember Wesley and the Sicilian in the Princess Bride, in the Battle of Wits). We keep games (unrealistically) one- shot, non-cooperative, complete information (but as we shall see not “perfect” information) – but that still takes us into very interesting territory.
The following set of clips, in order, introduces the basic idea of a simultaneous game and how to analyse it using a useful “mind-tool”, a payoff table, a way of thinking called best response reasoning , and a prediction of the strategic outcomes of the game called a nash equilibrium
Module 3 Topics (in order)
- 3.0 Brief Intro and “Perspective” , How a slightly different answer to the 6 questions defining various types of games – Simultaneous games of complete information
- 3.1 Who will contribute to a public good? A simple 2 player, 2 move (2×2) simultaneous game about charitable giving called the VCM game (Voluntary Contributions Mechanism game) ; PDIP introduces new ideas: payoff table ; using best response reasoning to analyze and predict ; dominance reasoning ; new prediction concept – dominant strategy equilibrium, pareto efficiency or inefficiency of strategic outcomes
- 3.2 Adding more moves – extending the VCM game to permit a limited amount of contributions rather than all or none ( best response analysis with bigger payoff tables)
- 3.3 : Changing the VCM game by introducing a “moneyback guarantee” if the aggregate level of giving doesn’t pass a publicized threshold – new strategic problem, multiple equilibria; new equilibrium concept – Nash equilibrium
- 3.4 :the Classic Prisoner’s dilemma (BBC In Our Time podcast on Game Theory)
- 3.5 : The general features of a Prisoner’s Dilemma – when there are no criminals or prisoners, just dominant strategies and missed opportunites
- 3.6 : How far can dominance reasoning take us? What happens in games where some (all?) players do not have dominant strategies (Parliament vs Reserve Bank game) ; dominance reasoning through iterated elimination of dominated alternatives; an example of dominance reasoning in practice: Vickery’s ideas about “telling the truth” – bidding honestly – in a second price auction
- 3.7 : Nash Equilibrium :our first defintion of Nash Equilibrium and its interpreation as a system of actions and belief ,
- 3.8 : Coordination games – basic ideas :colour matching game, multiple nash equilibria, and Schelling’s focal points,
- 3.9 : The standard 2×2 coordination games : pure coordination, assurance, stag hunt, chicken, battle of the sexes – includes an exposition of how to use payoff mtrices and best response reasoning for a 3 Person stag Hunt game
- 3.10 : Nash Equilibrium – Why? Why not? What about risk? doubts? What if no NE exist?
- Traveller’s Dilemma,
- Airport concessions and rugby matches,
- Battle of Wits
- The minimum effort coordination game