User:OrenBochman/WGT/Simple Games

Some simple games

Notation and requirement - we need

1. players $i,j$ (small letters)
2. strategies
   • $S_{i}$ all the strategies of $player_{i}$.
   • $s_{i}$ a strategy for $player_{i}$ where $s_{i}\in S_{i}$ .
   • $s$ is a particular play of the game (a strategy profile).
   • $s_{-i}$ is a particular play excluding the option of $player_{i}$
3. payoffs $U_{i}(s_{1},...s_{i}...s_{n})$ or abbreviated $U_{i}(s)$ 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

methodology involves

• 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.

Cooperation

• Coordination can be modeled by:

	Ban	Pass
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

$p_{ban}=\sum edits_{ham}-L\sum edits_{spam}$

	patroller (accept)	patroller (ban)
Editor GF (ham)	(0,0)	(0,0)
Editor BF (spam)	$(0,-(1-p_{ban})({\frac {work}{\lVert Community\rVert }}))$	$(-p_{ban}\times work,-p_{ban}({\frac {work}{10}}+coo))$

• 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).

Practicalities

note: there is a probability of getting an admin or an non admin reversion.