Logic, Co-ordination and the Envelope of our Beliefs

Abstract

Abstract Each of us has a story which we can think of as a set of beliefs, hopefully consistent. We make our decisions in view of our beliefs which may be probabilistic, in the general case, but simple yes or no as in this paper. Our beliefs are our envelope just as the shell of a tortoise is its envelope. Decision theory—or single agent game theory tells us when to make the best choice in a game of us against nature. But nature has no desire to further or frustrate our efforts. Nature is mysterious but not malign. Things change when there are other agents involved. Then the best thing for us to do will depend on what they do. And they will think the same. And we predict their actions in terms of what we think their beliefs are. But how do we coordinate with others whose beliefs are different? This paper addresses the issue of working together despite different beliefs.