Reviews for The mathematics of games of strategy

The average rating for The mathematics of games of strategy based on 2 reviews is 3.5 stars.

Review # 1 was written on 2017-05-08 00:00:00 Michael Morgan Remember that iconic scene in Wonder Woman, where she crosses No Man's Land amidst enemy bullets and inflicts damage at the other side. Well, she was ruining a relatively peaceful ecosystem built on mutual restraint over mutual punishment. World War I, on a national level, was a zero sum game where loss on one side meant gain on the other. But on local levels, specifically along the Western Front, between France and Germany, a curious system of 'live and let live' emerged. Trench Warfare, limited within narrow trenches few hundred yards apart, with all its disgusting horrors became the stage for something amazing in history- a classic example of reciprocal altruism in a world of unconditional defection. A feeling of solidarity developed among enemy soldiers over time, and it was characterized by ad hoc weather truces, common lunch times and even combined Christmas celebration. During Christmas Germans put up decorated table top trees over the trenches, and British-French soldiers responded by singing Carol songs. They left their weapons in trenches and came up to shake hands in no man's land; swapped presents, traded stuff, buried the dead, shared barrels of beers and cigars till the whole morning. In some portions along this hundreds of miles stretch, the period of goodwill lasted as long as a whole week. This restraint was not due to weakness, but rather the rationale of defection being self-defeating; much like modern day deterrence between Nuclear States over fear of mutually assured destruction. In this seminal work, Robert Axelrod, with unusual clarity discredits friendship or kinship as the essential necessities for cooperation based on reciprocity, even in inception stage. And argues that, under suitable characteristics, cooperative relationships can well arise even between antagonists. According to Hobbes, and other earlier political theorists like Rousseau and Locke, human beings are primordially selfish individuals, who competed among each other for their own solitary, brutal and short life. Strong central authority (Leviathan) later entered into society by rationality of mutual interaction and hence, however unnatural of basic human nature, is required for maintaining cooperation among individuals. One can argue against this with evolutionary and biological examples that show social cooperation being hardwired into living consciousness. What Axelrod did was to arrange a computer tournament for an iterated Prisoner's Dilemma problem and invite computer program strategies from his friends and colleagues. Prisoner's Dilemma is a thought experiment, a set of circumstances that forms the building block of Game Theory. In a Minority Report scenario, two potential prisoners are captured and interrogated separately for conviction. Each of them can stab the other in their back for lesser sentence or cooperatively deny for a favourable outcome of walkaway. The possible scenarios in ascending order of pay offs are as follows- unilateral defection from partner, mutual defection, mutual cooperation and unilateral restraint from partner. Since individuals cannot control the other person's behaviour, each player is in a dilemma whether to rat out ones partner for maximum pay off or to cooperate for the mutually preferable outcome. Game theory expands this to behavioural problem with mathematical formalities and tries to optimize strategies for negotiations in economics, diplomacy, biology, psychology etc. In Axelrod's tournament, various computer programs competed against each other for over 200 times in this non zero sum setting. In all the possible interactions one strategy came out dominant pushing every other programs into extinction and its relative success had nothing to do with its author or brevity or length. This simple strategy known, rather appropriately, as TIT for TAT, was just two lines of code. First line - be nice. Second line - do what the other player just did. So T4T starts off cooperating with the opponent and continue doing that till the other player defects. It will then defect and again switch back to cooperation once the opponent starts to cooperate. Though mathematically the optimum option is to defect in all moves, the nicer strategies was found to be outweighing the meaner ones in competition, with TIT for TAT dominating them all. It was a very robust program- nice to begin with, retaliatory when required, and was forgiving and clear; but not free of failures. A signal glitch or mistake in translation might cause a string of recriminations and counter recriminations between players employing T4T. So, it would be extremely important to reduce the echo effects while employing the strategy for high stake environments, as defection strings can cause escalations as far-fetched as Cuban Missile Crisis. A forgiving TIT for TAT was found to be effective, though not immune of exploitation, in such conditions, where it switches to a forgiving strategy after certain rounds of mutual defection. Axelrod argues that the maximization of outcome depends on characteristics of a particular strategy, nature of other strategies with which it most interacts and the history of interactions. Coming back to the Trench Warfare, No Man's Land basically represented a dynamic equilibrium of stalemate. The troops at both sides were large enough for accountability and small enough for controlling individual behaviour. Since not every bullet, grenade or shell fired in earnestness would hit the exact target, there was an inherent tendency towards descalation. Demonstration of retaliatory capacities and verbal arguements were internally suppressed by superiors, and during the rotation of troops, outgoing soldiers made it their business to familiarize the new recruits with the status quo. Infantries often offered delicacies for Artilleries as gentle incentives for not provoking the enemy side, since they were relatively safe with fewer stakes in this 'live and let live' system than them. And on a macroscopic scale, especially after the joint Christmas celebration, High Command of German, French and Britain wanted an end to these tacit truces as a pacified system will only sap morale from war's ceaseless policy of offense. Though I might come out as a heretic in this comparison, war time General's behaviour can be observed in Wonder Woman too whose primary objective was killing Aries. The immediate and extended payoffs for both Aries and Diana were big enough to justify their actions. Though offensive demonstrations and firings can be heard in background, there was no direct enemy attack towards the trenches, even in the movie depiction. And it was her crossing of No Man's Land that destroyed the truce and escalated the war on both fronts, killing the microscopic payoffs for macroscopic ones. Also, it would be worthwhile to note that the attack was instigated by outsiders (Trevor and Team) than the soldiers involved in the counterbalance, who might have been in the moral enigma of breaking their side of trust. Similarly in further history of actual WWI, High Command imposed raids and retaliatory efforts eventually collapsed the Trench Warfare system. Even during those orders for mandatory offense, ethics of cooperation was maintained keeping the per-functionary and routine firing aggressive enough to satisfy high command and contained enough to avoid any retaliation, as long as they could. Axelrod extended his computer simulation strategies into an evolutionary scenario, where winning program gets to create copies of themselves, and running them for many generations. Even in a horribly hostile world, if the nice programs had enough chance to interact, it was found that they can eventually take over the world full of meaner strategies. The beauty of altruistic behaviour in negative spaces can be observed in evolutionary biology as well. Though rational agents always defect in Prisoner's Dilemma, knowledge about options of other party drastically changes the scene. When third parties are watching, the stakes of current situation expands from those immediately at hand to the reputation and future interactions of players. Internet bullying under the mask of anonymity and friendliness a regular customer might enjoy in a shop can be considered as crude examples. Anyway it gets even more complicated with changing pay offs and concentrating interactions. I was constantly drawn towards Cixin Liu's Dark Forest deterrence theory and its aftermath in later installments of Three Body Problem, as my very own literary example for applying the half cooked nuances of game theory and prisoner's dilemma. Real world problems are far more complex than Axelrod's computer simulation, with multiple players and complex pay offs that demands sophistication in analysis. But this propensity for reciprocal altruism among antagonists was a theory robust and well-articulated enough to have my undivided attention. And this karma based upright, forgiving and yet retaliatory strategy is a nice take away for life, maybe with more leaning towards reconciliation.

Review # 2 was written on 2013-10-30 00:00:00 Cornelius Cook It's not overstating the case to say that Robert Axelrod's The Evolution of Cooperation is literally the most important book of the last 100 years and will change the course of human history. Um, Andy, I think you need to revisit the definitions of certain words, like "literally" and "overstating." OK, granted. But the implications of the game theory research and analysis presented here are so profoundly important, it's difficult not to descend into hyperbole. Or ascend, as the case may be. Sure, at first glance it appears to be an account of legions of math and computer nerds trying to beat one another at a silly game. Who would suspect that these nerds may have essentially discovered the philosophical glue that holds all of society together? And done so with programs written in just a handful of code lines written in BASIC and FORTRAN, no less? I did, but I cheated, of course. I was already convinced of game theory's profound significance before I ever picked this up. I was doing research, reading everything I could find on the subject for my own book about game theory, my premise being that these astoundingly important ideas might be better received if put in the context of a novel with snappy dialogue and lots of horrific violence. No horrific violence here, nor snappy dialogue either. Just a clear and lucid explanation of a very complex subject. Few of us will ever find ourselves in a literal equivalent of the prisoner's dilemma (PD), forced to decide whether to testify against a partner-in-crime to receive a lighter prison sentence. But we find ourselves in analogous situations literally every day, and mind you: I've double checked my usage of "literally" here and this time I'm sticking by it. These PD situations are so omnipresent they are virtually invisible, as are the long-established cooperative equilibria that prevent all of us from continuously stabbing one another in the back as we fall into the alluring Nash equilibrium of mutual defection, leaving behind vast hordes of stabbed people and a few smug mathematicians mumbling "I told you so" as they tend to their wounds. Even more important than providing a mathematical explanation of why (most) people aren't just total and complete pricks (please refrain from pointing out noteworthy exceptions. We all know some. Oftentimes I'm one of them.), and why we've been able to develop a complex society that could not exist without seemingly irrational altruism, modern game theory teaches us how we can create an even better society. Cooperation has evolved over the course of millions of years by participants lacking the slightest knowledge of game theory, or, indeed, opposable thumbs. Evolution is a highly effective way to produce desirable results without any thought or effort whatsoever, provided one has a few million years to spare and doesn't mind a lot of pain and suffering along the way. For beings with the cognitive abilities to understand the forces at play, they can achieve the same results far more efficiently. It's a very complex non-zero-sum game we're all playing. We can all score a lot more points if we play it right. …………………………… I'm going to stick in one last plug for my book, Practical Applications of Game Theory , which dramatizes an actual prisoner in prison facing a literal example of the prisoner's dilemma. It's full of math, snappy dialogue, and, I should reiterate: horrific violence.