# Strategy space

The strategy space of the players is created using a knowledge base to collect the sense inventories *S _{i}* ={1,...,

*m*} of each word in the text, where

_{i}*m*is the number of senses associated with word

_{i}*i*. Then, it creates the list

*C*=(1, . . . ,c) of the unique senses in all inventories, which corresponds to the space of the game.

With this information, it is possible to initialize the mixed strategy space *x* of each player. It can be initialized using a uniform distribution or considering information from sense labeled corpora, allocating more mass to frequent senses. In the former case, we initialize the strategy spaces of each player with the following equation:

*
*

In the latter case, we assign to each sense a probability according to its rank, assigning higher probabilities to senses with a high frequency. To model this scenario, we used a geometric distribution that produces a decreasing probability distribution. This initialization is defined as follows:

*
*

where *p* is the parameter of the geometric distribution and determines the

scale or statistical dispersion of the probability distribution, and *r ^{h}* is the rank of sense

*h*, which ranges from 1, the rank of the most common sense for word

*i*, to , the rank of the least frequent sense. These values are divided by

*^x*

*to make them add up to 1. In our experiments, we used the*

^{h}*heC*

ranked system provided by the Natural Language Toolkit (version 3.0) [BIR 06] to rank the senses associated with each word to be disambiguated.