---
bibtex: @article{eggers2011hobbes,
title={Hobbes and Game Theory Revisited: Zero-sum Games In The State Of Nature},
author={Eggers, Daniel},
journal={The Southern Journal of Philosophy},
volume={49},
number={3},
pages={193--226},
year={2011},
publisher={Wiley Online Library}
}
---
I shall subscribe to the view, advanced by Graham Dodds and David Shoemaker (2002), that Hobbes’s state of nature contains differently structured situations of choice, the game-theoretic representation of which requires the PD and its most discussed rival, the assurance game (AG), and the so-called assurance dilemma (AD). p194
(see his notes for lit review)
Criticisms of using game theory with Hobbes. Some suggest Hobbes' ethics was deontological.
It is correct that the application of game theory to Hobbes would be problematic and perhaps misleading if the behavior of Hobbesian individuals were restricted by moral obligations in the strict sense of the word, that is, by unconditional or categorical duties. p195
The mere fact that a person acts on strong passions, however, is not sufficient for her behavior to be irrational in the game-theoretic sense. p195
Hobbes' aim:
Hobbes’s purpose is to provide a justification for civil society and civil obedience with the help of a counterfactual scenario. His aim is to show that no rational individual can desire to live outside of civil society, not to show how a state of nature, should it ever fully obtain, can be left again. p197
If the purpose of Hobbes’s argument is to convince citizens of existing societies of the necessity of absolute obedience by painting the black- est possible picture of the relapse into a nonpolitical condition, then this argument can only be strengthened by the assumption that this terrible condition, if it ever fully obtains, can never be left again. p198
it seems that in order to assess Hobbes’s argument for the necessity of civil society, one can dispense with analyzing the rationality of covenant-keeping—even if one admits that there can and will be valid con- tractual agreements in the state of nature p198
Footnote on which text to focus on.
Given this, the Leviathan seems to provide the appropriate basis for a game-theoretic analysis of Hobbes’s discussion of anticipatory violence, the English version was chosen here mainly for the sake of convenience. p198
War isn't irrational.
Hobbes presents the violent competition for goods neither as a result of human irrationality and self-conceit nor as a result of a natural desire to dominate other individuals. p199
Note also that the equality of hope arises from the equality of ability.
The “equality of hope,” therefore, is due to a realistic assessment of one’s own abilities, to the modest and realistic view that one can, in principle, conquer a possible opponent and survive. p199
Hobbes does not seem to recognize any peaceful alternative course of action.
the individuals are led into such violent conflicts—at least sometimes—by the mere goal of self-preservation. p199
Dominators and moderates - even rational moderates protecting their self-interest leads to war.
The suggestion that modest or sensible individuals could refrain from settling the competition for goods with the use of force altogether and simply dispense with the goods in question is, therefore, irreconcilable with Hobbes’s account: the rational pursuit of self-preservation not only inevitably leads individuals in the state of nature into competition for goods that cannot be divided, it also leads them into deciding this competition with the use of force, and it even leads them into using anticipatory violence. p199-200.
Only partial scarcity of goods is necessary for Hobbes' argument. p204
The unwilling- ness to produce goods, however, may also by itself lead to partial scarcity, which again may become a cause of violence. p204
Once there is a sovereign power, therefore, individuals who cultivate their land and engage in other productive enterprises need not fear that they will lose the fruits of their labor as much as they need to fear it in the state of nature, which means that there is more of an incentive to make the relevant efforts. p205
Moreover, there can hardly be any doubt that the competition for goods and the necessity of preemptive violence are sufficientto turn the state of nature into a state of war—in Hobbes’s sense of the term—which suggests that the third source aggravates conflict rather than initiates it. p206
Appropriate games to model Hobbes must capture the paradox that no one wants war but rationality and competition drag everyone into it. p206
Eggers is explicit that he is using a one-shot analysis, not an iterated one. p208
Using a PD makes attack strictly dominant. But Hobbes suggests otherwise...
Rather, Hobbes’s view seems to be that the individuals should attack only because they cannot be sure that others will indeed behave peacefully. p209
Using a AG, it is rational to attack only when attacked. But this is known to all so it is irrational to preemptively attack. p209
But because life is at risk, it might be rational to minimax and choose preemption. p209
This would mean that in spite of the general reasonableness of peaceful behavior, Hobbesian individuals would strike out in order to avoid the outcome of unilateral not-attacking.
Motivation for my paper:
In order to account for the two other possible cases (viz., the encounter of two moderates or the encounter of two dominators), the AD needs to be supple- mented by the AG and the PD. Hobbes’s distinction between moderates and dominators, therefore, renders the enterprise of describing the problem of anticipation by the use of one single game matrix impossible: the problem of anticipation has the form of a PD whenever two dominators face each other, the form of an AG whenever two moderates face each other, and the form of an AD whenever a moderate and a dominator face each other. p211
Instead, all the games are required in order to describe the underlying situations of choice, a fact that has prop- erly been acknowledged only by Graham Dodds and David Shoemaker (2002). p220
The game-theoretic analysis of this particular problem reveals that, in addition to the occurrence of PD, AG, and AD situations, Hobbes’s natural state is plagued with other games as well, most importantly with zero-sum games in which mutual cooperation is straigh- forwardly impossible. p221
The application of game theory not only requires a particularly precise and thorough analysis of Hobbes’s statements but also furthers such an analysis by sharpening the view for the implications of those statements and for possible inconsistencies in Hobbes’s argument. p222
A more detailed use of game theory—one that would include more detailed mathematical descriptions and evaluations of the different strategies and outcomes—is prevented by the fact that Hobbes neither spells out these strategies and outcomes nor the actual reasons that lead the individuals to prefer one strategy over another with the accuracy required for such an analysis.
The game-theoretic analysis of Hobbes’s statements can help to show that and how individually rational behavior can lead the inhabitants of the state of nature into a state that is contrary to reason. p223
Egger's lemma
This matrix shows that type 3 situations represent zero-sum games in which no mutually cooperative strategy exists but in which one player necessarily loses what the other gains. Since Hobbes’s derivation of the state of war starts from such situations and since the necessity of anticipatory violence is depen- dent on their occurrence, it can be concluded that a full game-theoretic representation of Hobbes’s “war of every man against every man” needs to draw on the zero-sum game “competition for vital goods.” p220
The problem here is that if it is instrinsically zero sum, then a sovereign wont help. If it is contingently zero sum (ie that under a sovereign & therefore peace, scares resources become less scares) then we must also allow for the possibility of the same occuring in the state of nature!!!
In fact, there are good reasons to assume that situations of competition for necessary but scarce goods will strongly increase in number, given the overall increase in violent confrontations and their negative effect on human culture and human industry. p221