**Figure 1:** This is an example RMM hierarchy for two agents A1 and A2. The
leaves of the tree will either be Zero Knowledge (ZK) strategy or a
sub-intentional model. Note that we consider the ZK strategy and the
NO-INFO model in [8], as equivalent.

An example payoff matrix along with its RMM hierarchy, is shown in Figure 1. This RMM hierarchy represents a situation from agent A1's point of view and, therefore, has her payoff matrix at the root. Assuming that agent A1 knows something about how A2 represents the situation, then A1 will model A2 in order to predict his strategies, which will allow A1 to generate better strategies for herself. These models take the form of payoff matrices and are placed below the root node. The probability associated with each branch captures the uncertainty A1 has about A2. If A1 similarly knows something about what A2 might know about how A1 represents the situation, this could be further captured as more deeply nested payoff matrices, as implied in the left branch of the figure. If A1 knows something about what A2 expects A1 to do in the situation but not how A2 represents A1's thinking, then A1 could associate with A2 a sub-intentional model of A1 that summarizes A1's likely actions. Finally, If A1 believes that A2 has no knowledge of A1, this can be captures in a ZK strategy, as shown by the rightmost branch.

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jmvidal@umich.edu

Sun Mar 10 12:52:06 EST 1996