Talk:Signaling game

formal section corrected

I corrected the formal section on equilibrium which was badly done. (The dependence of the receiver's action on the sender's was not expressed, leading to a wrong formalisation.) Some minor edits too. The section is not as clear as it could be, but at least not wrong now. I added the possibility of mixed strategies (necessary for equilibrium sometimes), and take credit for the joke about mixed messages!

One point: I am not sure the message/action wording is the best: it seems to imply costless signalling (that different messages are equally costly). CSMR 03:46, 21 November 2005 (UTC)

I think the formal section is still wrong for the following reasons:

• Requirement 2 states that the receiver has to take action a^*(m) that maximises \sum_{t_i} \mu(t_i|m)U_R(t_i,m,a). But a^*(m) is defined as a probability distribution over the set of messages A (in my opinion this choice of notation is not felicitious). It does not make sense to say that a probability distribution maximises the above sum. It should at least be switched to the following: using the notation a^*(m)[a_j] standing for the probability for the receiver to play a_j given he has received message m<, For all m, probabilistic strategy a^*(m) for the receiver has to be a best response to m, i.e., has to maximises \sum_{t_i} \sum_{a_j} \mu(t_i|m) a^*(m)[a_j] U_R(t_j,m,a_i). Now this is feasible only if probabilistic strategy a^*(m) assignes non-zero probability to actions a that maximises \sum_{t_i} \mu(t_i|m)U_R(t_i,m,a) which is the formula has it appears now in the section. So I think there is a global confusion between a^*(m) seen has a probabilistic strategy on the one hand, and has a pure best response on the other hand, induced by the choice of notation.

• Notation U_S (t, m,a^*(m)) is undefined in requirement 3. My guess is that it means \sum_{a_i} a^*(m)[a_i] U_S(t, m,a_i). But once again, if m^* stands for a probablistic strategy, then this does not make sense, and it should be said instead that each m in the support of m^*(t) has to maximise the previous sum.

• Last and most important point I think; the Bayes formula exhibited in requirement 4 does not make sense at all. Assuming the undefined notation p(t_j) refers to the prior probability of the sender to be of type t_j, then \sum_{t_i} p(t_i) = 1 and p(t)/\sum_{t_i} p(t_i) = p(t) which do not make sense for \mu(t|m). The priors should be revised coherently with the belief of the receiver towards the sender's strategy, which in equilibrium is assumed to be m^*. Hence application of the Bayes formula should go as follows: For each message m_i if there is a t_j such that m^*(t_j)[m_i] ≠ 0 then \mu(t_k|m_i) = p(t_k)m^*(t_k)[m_i]/\sum_{t_j} p(t_j)m^*(t_j)[m_i]

Where is Zahavi?

As far as I know, according to Dawkins, A. Zahavi was the first to propose the handicap principle in regards to Birds of Paradise and Thompson's Gazelles. Even if future biologists have expanded upon the theory, Zahavi deserves initial credit for the ideas. (q.v. handicap principle)

If nobody objects, I will update the article accordingly. — MSchmahl… 11:57, 25 December 2007 (UTC)

Yeah, sure, go ahead. Though, in way of some defence of the present state, the article is about signalling games in a fairly strict game theory sense, and I don't think Zahavi's work (as undeniably influential as it is) is as "on point" as Grafen's work. Grafen's work applies game formal game theory, and a signalling game to the problem, along the lines suggested by Zahavi. Cheers, Pete.Hurd (talk) 05:48, 26 December 2007 (UTC)

Spelling

Shouldn't we use either British English OR American English? Signalling vs. signaling etc.? —Preceding unsigned comment added by 132.231.54.1 (talk) 14:58, 10 February 2009 (UTC)

Yeah, the WP convention is to consistently apply whichever spelling was discernably used first in the history of the article. Judging from the title, I'd guess that it is US spelling that should be used throughout this article. Pete.Hurd (talk) 19:12, 10 February 2009 (UTC)