Game Theory: players' gender convention?

Question

What is the Game Theory convention of using gender terms (male/female) for the players?

I found only one reference suggesting that odd-numbered players are male and even-numbered players are female.

Best regards,

Avner

Answer 1

I do not think that there is a common convention in the litterature. A good illustration of the divergence of opinions in the field can be found in the preface of A Course in Game Theory by Osborne and Rubinstein:

"A Note on Personal Pronouns

We disagree about how to handle English third-person singular pro- nouns.

AR [Ariel Rubinstein] argues that we should use a “neutral” pronoun and agrees to the use of “he”, with the understanding that this refers to both men and women. Continuous reminders of the he/she issue simply divert the reader’s attention from the main issues. Language is extremely impor- tant in shaping our thinking, but in academic material it is not useful to wave it as a flag, as is common in some circles.

MJO [Martin Osborne] argues that no language is “neutral”. In particular, there is a wealth of evidence, both from experiments and from analyses of lan- guage use, that “he” is not generally perceived to encompass both fe- males and males. To quote the American Heritage Dictionary (third edition, page 831), “Thus he is not really a gender-neutral pronoun; rather it refers to a male who is to be taken as the representative mem- ber of the group referred to by its antecedent. The traditional usage, then, is not simply a grammatical convention; it also suggests a par- ticular pattern of thought.” Further, the use of “he” to refer to an individual of unspecified sex did not even arise naturally, but was im- posed as a rule by (male) prescriptive grammarians in the eighteenth and nineteenth centuries who were upset by the widespread use of “they” as a singular pronoun and decided that, since in their opinion men were more important than women, “he” should be used. The use of “he” to refer to a generic individual thus both has its origins in sexist attitudes and promotes such attitudes. There is no neat solution to the problem, especially in a book such as this in which there are so many references to generic individuals. “They” has many merits as a singular pronoun, although its use can lead to ambiguities (and complaints from editors). My preference is to use “she” for all individuals. Obviously this us- age is not gender-neutral, but its use for a few decades, after a couple of centuries in which “he” has dominated, seems likely only to help to eliminate sexist ways of thought. If such usage diverts some readers’ attentions from the subjects discussed in this book and leads them to contemplate sexism in the use of language, which is surely an issue at least as significant as the minutiae of sequential equilibrium, then an increase in social welfare will have been achieved. (Whether or not this book qualifies as “academic material”, I see no reason why its readers should be treated differently from those of any other material.)

To conclude, we both feel strongly on this issue; we both regard the compromise that we have reached as highly unsatisfactory. When re- ferring to specific individuals, we sometimes use “he” and sometimes “she”. For example, in two-player games we treat player 1 as female and player 2 as male. We use “he” for generic individuals."