The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player~2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage.
Blackwell and Ferguson (1968) give an epsilon-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends just on the clock or on a finite memory is worthless.
The long-standing natural open problem has been whether every strategy that depends just on the clock and a finite memory is worthless.
The present paper proves that there is such a strategy that is epsilon-optimal.
In fact, we show that just two states of memory are sufficient.
We provide an elementary mathematical description of the spread of the coronavirus. We explain two fundamental relationships: How the rate of growth in new infections is determined by the “effective reproductive number”; and how the effective reproductive number is affected by social distancing. By making a key approximation, we are able to formulate these relationships very simply and thereby avoid complicated mathematics. The same approximation leads to an elementary method for estimating the effective eproductive number.
We use response curves in a repeated game to analyze key aspects of mutual deterrence: escalation, de-escalation, incomplete deterrence, and deterrence by denial. In this approach, episodes of violence are due to interacting response curves, which disincentivize opponents from attacking through both deterrence and compellence. Both sides punish attacks to maintain credibility in future episodes, disincentivizing larger attacks and yielding nonviolent lulls. We empirically estimate those curves using detailed incident data from the Israel-Gaza conflict between 2007 and 2017. Our estimates match the dynamics of the raw data: very frequent episodes of low lethality violent exchange. Response curves are stable and probably Markovian. They exhibit a posture consistent with incomplete deterrence: i.e., episodes de-escalate, but to a violent equilibrium. Israeli missile defense shifts the Gazan response curve to a less aggressive posture, as predicted by theory.
This paper studies the long-term effects of politically motivated violence on individuals’ political attitudes focusing on the Second Intifada (2000 – 2005). We conduct a large-scale survey that measures Israelis’ attitudes today and elicits their places of residence since 1985. The survey allows us to measure individuals’ direct exposure to terrorism and to account for potential selective migration. This, in combination with the fact that individuals’ characteristics are balanced with respect to their exposure to terrorism, enables us to overcome identification concerns and provide credible estimates of the causal effects of the Intifada on attitudes. The results indicate that exposure to terrorism during the Second Intifada caused a persistent and substantial shift toward right-wing attitudes that is still observable two decades later. Thus, our analysis provides systematic empirical evidence supporting the view that the Second Intifada soured a generation of Israelis on the idea of peace.
This paper assesses the validity of narrow deterrence theory between a State and a Non-State actor in the context of the Israel and Gaza conflict. We build the most comprehensive data set on this conflict between 2007 and 2014 using original security reports from the United Nations, which capture over 16,000 Palestinian projectile launches and over 8,800 Israeli airstrikes, recorded with precise timing. We show that this conflict is characterized by short-lived episodes of violence separated by quiet interludes. Episodes tend to last less than one day and are followed by 3.5 days of calm, on average. Most episodes have no retaliation and consist only of provocations that go unanswered. Moreover, counter-retaliation does not induce subsequent episodes. We find that Israeli retaliation strongly correlates with Gazans’ initial number of attacks and type of rockets fired. Yet, rather than provoking an immediate increase in violence or de-escalation, retaliation seems to have no short-term effect. These findings support the concept of narrow deterrence and weigh heavily against the argument that retaliation perpetuates this conflict.
The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage. The undiscounted Big Match has been much-studied. Blackwell and Ferguson (1968) give an epsilon-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends on just the clock or just a finite memory is worthless (i.e., cannot guarantee strictly more than the least reward). The long-standing natural open problem has been whether every strategy that depends on just the clock and a nite memory is worthless. The present paper proves that there is such a strategy that is epsilon-optimal. In fact, we show that just two states of memory are sfficient.
