In a recent blog article, we discussed how banks' lifetime expected credit loss estimates, might be expected to increase, under various assumptions about the future. In particular, there exists a question of whether banks should assume a “U” or “V” scenario – for accounting values, as well as in setting their strategic behaviour. At the time of writing, there is a scarcity of information in the market that could help firms to conclude on the likely path of the credit cycle index (CCI) - be it "U", "V" or some other path.

Game Theory

The scarcity of information approaches idealised “laboratory conditions” or the textbook scenarios of game theory. We, therefore, explore a game played by two market participants, who may each adopt a set of strategic behaviour consistent with “V” or “U”. Importantly, we relax the common assumption that the CCI is purely exogenous, and assume that the other player’s actions feed through the inter-connected network of market participants (including banks and the real economy).

  • If both players choose “V” then balance sheets are relatively unconstrained and strategic behaviour is expansionary. Sufficient credit flows to the real economy, and both players benefit equally from the resultant CCI path.
  • If both players choose “U” then balance sheets become constrained and strategic behaviours become defensive. Credit to the real economy is constrained and a ripple of defaults occurs, significantly impacting both players’ payoffs.
  • If the players differ, then the payoff is more complex. The player that chooses “U” adopts defensive strategic behaviours, mitigating the impact to their payoff, with respect to the second scenario’s payoff. However, this also triggers a feedback loop into the real economy, which eventually impacts the player choosing “V”. Because the player choosing “V” had bet on expansionary strategic behaviours, they are over-exposed to credit risk and suffer more than in the second scenario. The player choosing “U” benefits less than in the first scenario, but fares better than the second scenario.

The following payoff matrix can, therefore, be assumed (recognising that in practice there is some subjectivity about the value of each payoff):

Player 2



Player 1







This is equivalent to the “stag hunt” game described by the philosopher Jean-Jacques Rousseau. The game differs from the perhaps more-familiar “prisoner’s dilemma” because two Nash equilibria arise. Absent any coordination, each player’s strategy will depend on whether they wish to maximise value, or minimise risk.

With sufficient coordination (and belief in the other player’s word), a player is therefore likely to select “V” and adopt the associated strategic behaviours. But without sufficient coordination and belief, a player is more likely to select “U”. Conditional on the payoff assumptions, a player’s best response switches from “V” to “U” at the point where the probability of the other player choosing “V” falls below 50%.

Consensus Herding

In practice, the economy is an interconnected network with more than two market participants spread across a number of reasonably homogenous sectors; and the “laboratory conditions” of the game theory problem are unlikely to hold, even with the current scarcity of information. It seems likely that market participants will instead herd towards consensus scenarios, such as the referenced scenario published today by the UK Office for Budget Responsibility (OBR) – this achieves a similar result to coordination between the players described above, by setting out prior beliefs about the probability of “U” or “V” for each sector in terms of Gross Domestic Product (GDP) impacts per sector.

Firms should, however, note that the OBR forecast assumes that the shocks to GDP reduce proportionally, conditional on restrictions being eased, with a return to pre-crisis levels in the fourth quarter. This aligns to our model’s upper forecast and is a reasonable assumption for an aggregate forecast, but may not hold for granular segments:

Example: Airlines

Any aggregate forecast can mask significant variations in the underlying population, especially if that population is known a priori to be heterogeneous.  Banks with exposure to particular sectors (e.g. leisure and discretionary travel businesses, and their employees) should consider sector-specific outlooks in internal scenario-analyses.

Market-implied Estimated Default Frequencies (EDFs) should already reflect public and private information about sectors and single names - including exposure to fuel prices, and whether strategic responses (such as downsizing airliner fleets, or mothballing less fuel-efficient aircraft) increase or decrease credit risk.