# User:OrenBochman/WGT/Simple Games

## Some simple games

Notation and requirement - we need

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

methodology involves

##### Cooperation
• Coordination[1] can be modeled by:
 Ban Pass Escalate 5, 5 0, 4 Pass 4, 0 2, 2 Fig. 1: Stag hunt example

#### 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

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

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

## Gloassary & Notes

1. 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

## Refrences

1. Cite error: Invalid <ref> tag; no text was provided for refs named Hoffman2010