The Price of Anarchy

As Computer Science, Information Technology, and the internet become increasingly important in, and vital to, the global economy, there are many concepts that will translate into significant political- and policy-relevance  in particular, for libertarians and anarchists. In the field of Algorithmic Game Theory and Mechanism Design, there is an important measure of inefficiency in a system known as ‘the Price of Anarchy’. Algorithmic Game Theory and Mechanism Design lie at the intersection of Computer Science and Economics and the common solution concept used in both is that of a ‘Nash equilibrium’. A Nash equilibrium, broadly speaking, is a situation where there is no player that has a unilateral incentive to deviate from their action (strategy), given the actions of all the other players.

In Economics (although ‘Applied Economics’ would seem to have more observable influence and immediate impact) it is ‘Economic Theory’ that has the most profound and lasting impact from a historical perspective (whether that be from the likes of John Maynard Keynes, Milton Friedman, Ludwig von Mises, Adam Smith, or Karl Marx, for example). In our world, where Computer Science, Information Technology, and the Internet are of central importance, it will not be long before the Price of Anarchy is raised in theoretical debates on economic policy and public policy more broadly.

A game is a strategic interaction between agents. The Price of Anarchy is a measure of inefficiency in a system where the outcome of a ‘centrally-planned’ solution is compared to the worst-case ‘decentralised’ solution in a game where players are seeking to minimise their own individual costs. The ‘social cost’ is the sum of the individual costs. The Price of Anarchy is the ratio of the social cost in the worst-case Nash equilibrium (the one with the worst social cost when selfish, individual players seek to reduce their own costs) to the solution that would have the lowest social cost if it were implemented by a ‘central planner’. The situation with the lowest social cost may also not necessarily be a Nash equilibrium.

In games where selfish agents are seeking to minimise their own individual costs, the Price of Anarchy will always be greater than or equal to one. This means that there will, quite often, be a lower social cost if the outcome was imposed by a central planner versus it being determined by rational, self-interested agents.  Quite recently, there has also been work done on the upper bound of the Price of Anarchy in Games of Incomplete Information; essentially, some of the key results there include the worst-case scenarios in certain games. One re-affirmed result is that, in a Generalised Second-Price Auction, the expected welfare of every Bayes-Nash equilibrium (the solution concept most commonly employed in games of incomplete information) is at least 1/4 times the expected maximum welfare. New results from that paper include bounds for routing games with incomplete information. Also of interest to readers may be ‘The Possibility of Cooperation’ by Michael Taylor which is an anarchist look at game theory (thanks to Emmi Bevensee for making me aware of this).

If the Price of Anarchy in a system is found to be relatively high, it can be used as a justification for those who advocate imposed, central planning instead of a ‘decentralised’ solution; this is of obvious concern to those who are inclined toward political philosophies of the libertarian and anarchist variety. Then again, the worst-case scenario is just that – the worst-case – the average-case scenario will generally be much better than the worst-case. Essentially, we must consider how the positive (as opposed to normative – though the two are inevitably interrelated in social sciences) difficulty of inefficiency can be overcome from various perspectives in order to enable the rational bolstering of the normative desirability of agents’ unrestricted autonomy. Essentially, we should now be aware of the future challenges that the Price of Anarchy can pose for those who seek expanded (and, ultimately, absolute) social and economic freedoms; as such, we can seek to formulate perspectives and arguments that are mindful of Price of Anarchy analyses as potential objections (possibly even by seeking to improve the Price of Anarchy bounds in other strategic contexts – whether that be mathematically or otherwise).

The academic-industrial complex in public policy (and across society more broadly) is immensely influential and this topic is particularly relevant to those who seek to defend and fight for freedom in particular technical domains. Indeed, being aware of scientific concepts that can potentially be used to limit autonomy, it would be foolish not to consider how we might both riposte and sustainably defend our beliefs. Anything less would amount to leaving social and economic freedoms unnecessarily vulnerable to sustained assaults in an ever-changing world.

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