A note on the structure of V(6) maps

The purpose of this note is make Theorem 13 in the article "On Biautomaticity of Non-Homogenous Small-Cancellation Groups" more accessible. Restatements of the theorem already appeared in few of the authors' succeeding works but with no details. We wish in this note to give the necessary details to these restatements.Comment: 8 pages, 3 figure

A volume estimate for the set of stable lattices

We show that in high dimensions the set of stable lattices is almost of full measure in the space of unimodular lattices.Comment: 6 page

The Talmudic Prisoner\u27s Dilemma

We argue that there is a stream in the Talmud that attributes the responsibility to one player alone in the case of a joint crime/joint tort and even in dividing the credits for a joint Mitzvah. We used the game theory to investigate which incentives are provided by this approach, which games are created, which games are blocked, and to which results this approach leads. In this paper, we present some Talmudic games. Although in Jewish law, a sinner cannot be a witness, one Talmudic rabbi proposes a rule that, in the case of a joint crime, one of the criminals may testify against a friend (who is the other criminal), but the court will not recognize the self-incriminating part of the testimony. The testimony of the criminal will also neutralize the friend\u27s capacity to testify against the criminal since the friend will be considered a sinner after the initial testimony. We argue that this rule may lead to maximal deterrence. We also investigate other Talmudic rules that impose responsibility on (only) one partner in the case of a joint deed: the halachic rule, which imposes responsibility in the case of bribery on the taker only. Another Talmudic rule that imposes the responsibility on the last player and only in the case of a joint murder/tort/mitzvah that was performed sequentially and the rule that imposes responsibility (only) on the agent and not on the sender. We also investigate the different rules about imposing responsibility on the partners who did not cover a pit. Surprisingly, there are rules that impose responsibility on only one partner, and we argue that this prevents a prisoner\u27s dilemma. This paper is a part of the developing field of the Talmud and Game Theory