Knowledge and Structure in Social Algorithms ( Extended

The first third of the XXth century saw two important developments. One of these was Ramsey’s tracing of personal probabilities to an agent’s choices. This was a precursor to the work of de Finetti, von Neumann and Morgenstern, and Savage. The other one was Turing’s invention of the Turing machine and the formulation of the Church-Turing thesis according to which all computable functions on natural numbers were recursive or Turing computable. Game theory has depended heavily on the first of these developments, since of course von Neumann and Morgenstern can be regarded as the fathers of Game theory. But the other development has received less attention. This development led to the development and design of computers and also to fields like logic of programs, complexity theory and analysis of algorithms. It also resulted in much deeper understanding of algorithms, but only computer algorithms. Social algorithms remain largely unanalyzed except in special subfields like social choice theory or fair division [2]. These fields do not tend to analyze complex social algorithms as is done in computer science. A later development, going back to the work of Hintikka, Lewis and a little later Aumann [5, 6, 1], brought in the issue of knowledge. The notion of common knowledge is of course very important for Aumann as common knowledge of rationality can be seen as a justification for backward induction arguments. But knowledge too has received less attention than it might. We all know that the Plame affair had something to do with someone knowing something which they should not have, and someone revealing something which they should not have. But why should they not? Clearly because of certain possible consequences. Knowledge and knowledge transfer are ubiquitous in how social algorithms work. We will try in this paper to bring attention to the importance of the two issues of knowledge and logical structure of algorithms, and show the way to a broader arena in which game theorists might want to play. Hopefully, in fact almost certainly, there is a rich general theory to be developed.