What do the Cold War powers of the United States and the USSR have in common with modern day asset managers? The capacity for mutually assured destruction. During the 1950s game theorists described a model of strategic interaction to demonstrate how it might be that two nations would choose to annihilate each other in nuclear conflict. Simply put, each nation had an incentive to strike first, as there was no incentive to retaliate. Both would race to push the button. Asset managers face a similar set of incentives.
The strategic interaction of these two superpowers was subsequently formalised as the “prisoner’s dilemma” by Albert W. Tucker. In the prisoner’s dilemma, two rational decision makers choose to pursue an uncooperative course of action that is detrimental to both, rather than cooperate to arrive at a preferable one. The reason the two parties can arrive at such an outcome is that for each individual, it is always better not to cooperate than to cooperate, regardless of the course taken by the other.
In the original thought experiment, there are two prisoners facing conviction of a crime, but they are suspected of a greater one. The sentence for the less serious offence is two years. Each is offered a deal: snitch on your friend for the greater of the two crimes and you can go free. But your friend gets seven years. If both snitch, both gets five years. So, to snitch or not to snitch?
What is clear is that it is better for both to keep quiet, and get two years, than for both to snitch, and get five each. Yet snitching is the ‘rational’ outcome; it’s the best strategy for me regardless of what my partner does (notwithstanding the risk of reprisals after the seven years I’ve spent in the Bahamas while my partner been behind bars).
Table 1: The prisoner’s dilemma
|Player 1||Don’t snitch||2, 2||7, 0|
|Snitch||0, 7||5, 5|
But what does that have to do with the asset management industry? Well, arguably, because it may, under some circumstances, be possible to characterise the coordination problem faced by asset managers as a prisoner’s dilemma. That stems from two factors. The first, relates to the high degree of concentration of the asset management industry – which results in potential spillovers from the actions of one asset manager to the payoffs of others. The second, relates to incentives arising from the practice of using peer comparison across individual asset managers to monitor performance – which make relative payoffs important.
The combination of these two features of the market could give rise to a situation in which, in period of financial stress, when there are concerns about falls in asset prices, rather than hold one’s nerve and stand pat, individual asset managers might reason that it is preferable to sell instead. If all asset managers reason thus, the resulting rush for the exit – and downward pressure on asset prices – could result in considerably bigger losses for everyone, than if asset managers had coalesced on the cooperative outcome.
Putting this interaction in a formal context, in the asset manager game below, in a period of financial market stress, anticipating that there may be a fall in asset prices, each player can either hold his (or her) position, or sell. In the event that both hold, each receives a loss of 1. But each also has the option of selling, in the hope of being first out of the door. If successful, that player reduces his own loss to 0, but increases the loss suffered by the other player to 2. If both players sell, this is the worst outcome of all (each loses 3).
Table 2: The asset manager’s dilemma (players’ relative payoffs are shown in red)
|Player 1||Hold||-1, -1
Now, this isn’t quite the same as the prisoner’s dilemma above. In the classic example, the bad outcome occurs because it makes sense not to cooperate no matter what the other player chooses. Here, it is possible that both players will be greedy and sell – gambling that the other will hold. But if one player knows that the other will sell, it would not be rational to sell as well. This would increase that player’s own loss from 2 to 3. The greedy player will simply be allowed to get away with it. So what would make it in the interest of player 1 to make losses even worse by choosing to sell as well?
This is where the practice of benchmarking comes into play. Asset managers tend to monitor performance against each other or against common benchmarks, to help investors compare investment propositions. As a result, benchmarking creates an externality in which the performance of one’s peers, affects one’s own payoffs. And it becomes in an individual asset manager’s best interest to minimise deviation from the rest of the pack – because his (or her) reputation and ability to raise a new fund and operate henceforth are a function of relative performance.
Now, in ‘good’ states of the world (the cooperative outcome, or the outcome in which the greedy gamble pays off) the externality does not affect behaviour: if an asset manager cooperates, or successfully cheats, his performance is either as good, or better than that of his peers. “Look at me! I’m doing at least as well as the other guy!” Happily, here, the asset manager’s incentives are aligned with those of the investor.
But, importantly, in ‘bad’ states (non-cooperation, or being cheated on), if one’s opponent is cheating, it is preferable to cheat as well, and both incur a big loss, than to be cheated on and incur a smaller loss. Better that, than stand out as an underperformer and risk losing one’s livelihood. “Well, we all did terribly. See you at the fundraiser!” As a result, selling will be that much more widespread, and asset price falls that much bigger, than otherwise. The asset manager’s incentives are not aligned with those of the investor.
Formally, each individual player’s preferred outcome is to cheat successfully (A). And each player prefers small losses (B) to big losses (C). But each would also prefer that both incur a big loss, than see the other profit at his own expense (D). A is preferred to B, B to C, and C to D. This is the general form of the classic prisoner’s dilemma (Table 3). Regardless of the decision of Player 1, it is in the interest of Player 2 to sell. For the investor in the asset manager game, however, it is clear that this represents a pretty miserable outcome.
Table 3: The general form of the prisoner’s dilemma
|Player 1||Hold||B, B||D, A|
|Sell||A, D||C, C|
The question then, is how to align the incentives of the asset manager with those of the investor? The cooperative outcome becomes more likely, if each player’s rewards reflect the absolute return generated by the fund, rather than performance relative to benchmark. This at least takes away some of the incentive to engage in mutually disadvantageous strategies, although greed on its own is still sufficient to yield the ‘sell, sell’ result.
To reduce the likelihood of that from happening, the academic literature on the prisoner’s dilemma suggests that in games where strategies are pursued on a probabilistic basis, a cooperative equilibrium becomes possible. Mechanisms which lower the probability of ‘sell’ might help to nudge players towards the jointly preferred outcome.
Moreover, cooperative outcomes also sometimes result from repeated games of the prisoner’s dilemma, provided that the end point is not known (otherwise players reason that it makes sense to cheat on the last game, and knowing that the other player will reason thus, infer that it will also make sense to cheat in the penultimate game, and so on, right back to the very first interaction). So perhaps we should embrace opportunities for players to arrive at the cooperative outcome; a little volatility may not be a bad thing.
Thomas Belsham works in the Bank’s Foreign Exchange Division.
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Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.