Chapter 5: Signaling Games    Run the Simulator   Source Code

Skyrms asks us to imagine a the evolutionary version of a signaling game (after David Lewis) in which one player knows what's going on and sends a signal to the other player, who must choose what to do based on the signal. In the simplest case, there are two states of the world that the first player percieves, two signals that can be sent, and two possible acts. We stipulate that it is best to do Act1 in State 1 and Act 2 in State 2. (Imagine if you like that the states are danger and no-danger, and that the acts are flight and no-flight.) There are, then, four strategies for sending and four strategies for receiving, as in the first table.

We imagine that each player has an equal chance of being sender and reciever, so that each player must have a complete strategy that consists of a sender strategy and a reciever strategy. Since there are four of each, there are sixteen possible complete strategies.

Complete Strategy	1 Sig1	2 Sig2	3 Anti1	4 Anti2	5	6	7	8	9 Free1	10 Free2	11	12	13	14	15	16
Sender Strategy	1	2	1	2	1	2	1	2	3	3	3	3	4	4	4	4
Reciever Strategy	1	2	2	1	3	3	4	4	1	2	3	4	1	2	3	4

In the case Skyrms borrows from Lewis, we are to imagine that this is a cooperative game, which is to say, the sender gets as much as the receiver out of the receiver performing the best act. Specifically, both players get a payoff of "1" when the receiver performs the best act, and "0" otherwise. In such a case (as you can see from the simulator) the system converges to one of two states - all Strategy 1, or all Strategy 2. Strategies 1 and 2 are "signaling" systems, and do very well against themselves (since the reciever always does the right thing). Strategies 3 and 4 are "anti-signaling systems" which always do the wrong thing when playing against themselves. They do well when playing against another, so that there is an unstable polymorphic equilibrium with 50% Strategy 3 and 50% Strategy 4. The equilibrium is unstable because adding just a little of either of the signaling systems to the mix results in them taking over the population. So from any initial mix of all sixteen strategies, you end up with everybody playing the same signaling (system) strategy, which looks like good news for the evolution of meaning.

But then, this seems a little too easy. After all, if the signal is something like a danger signal, then not only should the sender not get as much benefit than as the reciever, but a cost should be incurred. Skyrms discusses this case with regard to a four-state game, but we will stick with the two-by-two game. By clicking on the  <altruist/advanced> button, you change the rules (and add a couple of new controls as well). We imagine that the sender knows what is going on, so gets the payoff for doing the right thing, no matter what signal she sends. But sending signal 2 incurs a cost which is the risk of drawing attention to herself. Keeping silent (signal 1) is advantageous, so why bother if you don't get anything out of it? The signaling systems (1 and 2) don't do so well in these conditions. Of special interest are the two "free rider" strategies, 9 and 10. Each one is able to take advantage of the costs incurred by signalers, but stays quiet when it is their turn.  By changing the phase portrait to include one of the free rider strategies and clicking on points on the phase portrait, you can see that free riders take over when paired with the matching signaling system.

But what happens if strategies are more likely to play against themselves? (See the documentation for the chapter 1 model.) Seems that a little viscosity can   cause signaling systems to stabilize even in the presense of costs and free riders. You will see, however, that the cost of the signal makes a difference in how much viscosity is needed.

By clicking on the <altruist/advanced> button you can also do some things that aren't in the book (as it were). You can change the payoffs (just click the <change payoffs> button after you have modified the payoffs in the textfields). The matrix isn't labeled, but it follows the usual conventions:

This is a useful modification to make if you think (for instance) that it would be odd if the payoff for failing to avoid an actual predator (A1/S2) was the same as the payoff for unnecessarily fleeing (A2/S1). 

Finally, you may have noticed that we have been assuming that senders have perfect information, that is, their perception never fails. That's what's reflected in the default signal reliability matrix.

The reliability matrix does two things. It determines the likelihood of a sender mispercieving the state, but it also determines the relative frequency of the two states. The sum of the State 1 row is just the chance of the world being in state 1. Note that the four cells of the reliability matrix need to add up to 1, but the program takes care of this for you when you hit the <change reliability> button. Between the payoff matrix and the reliability matrix, you have enough control to take you a long way in investigating how these systems work. (This is mostly uncharted territory, as of the present, though some work in signal detection theory is making headway.)

One point of clarification: clicking on the phase portait starts the simulator with only the three face strategies represented, and since there is no mutation what you see is what happens with only those three strategies competeting. Use the <random start> buttons to start the simulator from points in the interior where all strategies are present.