Some simple games
Notation and requirement - we need
- players (small letters)
- all the strategies of .
- a strategy for where .
- is a particular play of the game (a strategy profile).
- is a particular play excluding the option of
- payoffs or abbreviated using a specific play
what we'd like to find out is:
- What would be the rational outcome
- dominant strategies
- weakly dominant strategies.
- mixed strategies
- sub-game strategies
- any the equilibrium (nash, etc).
- ESS (dynamically stable solution)
- Can payoff design be used to change the rational behaviour.
- How fragile is a wiki game to invaders[note 1]
- figuring out comes, followed by numeric payoffs and then parametric payoffs
- identifying well-known games
- solving for equilibria via http://www.gambit-project.org/doc/index.html
- solving ess etc.
- Coordination can be modeled by:
|Escalate||5, 5||0, 4|
|Pass||4, 0||2, 2|
|Fig. 1: Stag hunt example|
- a Stag hunt subgame.
- Very similar to a prisoners dilemma. But has two pure Nash equilibria and one mixed strategy Nash equilibrium.
The Normal Form Subgame
This sub game happens after an inciting incident sequence . This could be a spam edit or a perceived spam edit. An edit war may incite a block and repeted incident my incite a ban.
- under normal circumstances the user would only be banned in a spam incident. though it could also happen for other reasons those are
other types of ban games.
- the full game would add a second step where the Patroller bans the Editor with probability
|patroller (accept)||patroller (ban)|
|Editor GF (ham)||(0,0)||(0,0)|
|Editor BF (spam)|
- a patroller who bans a user incurs a coordination cost COO.
- the spammer only incurs the cost of setting up a new account estimated at one work unit.
- not banning a spammer has marginal cost (his future damage to the community).
note: there is a probability of getting an admin or an non admin reversion.
Gloassary & Notes
- good faith and bad faith invaders should be considered. Note: bad faith are obviously bad, would too much good faith be counter productive and render the population fragile to subsequent invasion
- Cite error: Invalid
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