# User:OrenBochman/WGT/Attrition

## Edit Wars

We can model edit wars using a war of attrition model, this is a model originally formulated by John Maynard Smith,[1] a mixed evolutionary stable strategy (ESS) was determined by Bishop & Cannings.[2] Strategically, the game is an auction, in which the prize goes to the player with the highest bid, and each player pays the loser's low bid (making it an all-pay sealed-bid second-price auction).

In the context of an edit war it is best to consider the dynamic formulation:

Two players are involved in a dispute:

• The value of the object to each player is ${\displaystyle v_{i}>0}$.
• Time is modeled as a continuous variable which starts at zero and runs indefinitely.
• Each player chooses when to concede the object to the other player.
• In the case of a tie, each player receives ${\displaystyle v_{i}/2}$ utility.
• Time is valuable, each player uses one unit of utility per period of time.

The evolutionary stable strategy is a mixed ESS, in which the probability of persisting for a length of time t is:

${\displaystyle p(t)={\frac {1}{V}}e^{(-t/V)}}$

As is the case with ESS - it does not guarantee the win; rather it is the optimal balance of risk and reward. The outcome of any particular game cannot be predicted as the random factor of the opponent's bid is too unpredictable. That no pure persistence time is an ESS can be demonstrated simply by considering a putative ESS bid of x, which will be beaten by a bid of x+${\displaystyle \delta }$.

### Interpretation

Wikipedia has often been described as a space where content of articles is decided by the most persistent editor. However in a war of attrition - all players must pay a price to participate and the winner can end up with a Pyrrhic victory.

Some open question for this model:

1. What is the utility assigned to articles by editors.
2. What factors affect this utility. (Considering a block, page protection, admin action, sanction may result from a content dispute, and that it may spread to other articles.)

## References

1. Maynard Smith, J. (1974) Theory of games and the evolution of animal contests. Journal of Theoretical Biology 47: 209-221.
2. Bishop, D.T. & Cannings, C. (1978) A generalized war of attrition. Journal of Theoretical Biology 70: 85-124.