Venture Capital trends mimic Nash equilibrium

Game theory studies rational agents’ interactions in various environmental settings. Many business problems can be formulated in a game theory fashion, but in order to be able to study them, researches have to narrow the real world complexity by 1) limiting the freedom of agents’ actions and 2) omitting many long-term and second-order effects originating from the environment. Due to the simplification often models obtained are hardly applicable to real life business problems. Otherwise we would have already lived in the world of highly efficient markets where all decisions are made by computers.

Despite that the assumption of agents’ rationality generally doesn’t hold, sometimes the evidence of the deal world playing optimal rational strategies can be observed.

VC trends

Trend 1. VC is exposing the tendency to focus more on late-stage companies rather than on seed & early-stage startups [1].

(1) Late-stage investing is outpacing early-stage [1]

Trend 2. Follow-on VC financing prevails considerably first-time financing [2].

(2) Follow-on VC investment soars while first-time remains almost unchanged [2]

Trend 3. Additionally, mega-deals set new records all over the world [1].

(3) Deal volume rises while deal number declines [1]

These trends demonstrate rising wealth inequality from another angle, but what are the underlying reasons behind them?

Hypothesis

I believe we observe here a repetitive non-zero-sum game, which VC firms play with entrepreneurs.

• The agents here are VCs on the one side and entrepreneurs on the other
• The actions of VCs are 1) funding startups 2) exit deals (M&A, IPOs) and entrepreneurs’ actions are 1) business decisions leading to a company growth 2) preparation for a quick & lucrative exit
• It’s a non-zero-sum game because basically neither side wins at the expense of the other: when a startup grows VCs invested in it do not lose but celebrate, and vice versa, when a VC fund makes money entrepreneurs likely expect additional VC support rather than the end of relationships
• It’s a repetitive game because of the continuous investing rounds and valuations

Now it resonates with an iterated prisoner’s dilemma — a one-shot prisoner’s dilemma game played many times by the same participants.

In one-shot prisoner’s dilemma pictured below the rational strategy i.e. Nash equilibrium is the mutual defection — each self-interested player could only do worse to himself by unilateral deviation from his strategy [3]. But as we see, and that’s why we have dilemma in the game’s name, they’d better cooperate together.

(4) One-shot prisoner’s dilemma [3]

If the game is played a fixed number of times and both players know this number, then the rational strategy is again — always defect.

BUT, when we have an infinite repeated game, or in other words, players don’t know from the beginning how many iterations they’re going to play (like in real life) then the rational strategy is to cooperate first then subsequently replicate the opponent’s previous move (aka tit for tat). This scheme protects each player from large losses by having punishment mechanism which triggers only when the other player is greedy. The strategy stays relevant until the discounting factor of future rewards is low enough, but breaks when the players value today’s payoffs much higher than tomorrow’s.

How the trends support the hypothesis?

We’ve observed market trends of VC shifting focus from investing in early-stage startups to investing in late-stage robust businesses and also soaring follow-on % of VC investments. What these trends tell us?

• The incentive of VC here is to play the long-term game, because capital compounding requires time
• Late-stage businesses have more chances to play the long-term game, especially in digital businesses where steadily growing customer base reinforces their competitive advantage due to the network effect
• No one wants to be defected by the other
• The actual duration of VC and entrepreneur relationship is unclear to both at the beginning

Therefore VCs and entrepreneurs end up playing this long-term wealth creation game together, because they don’t have to believe each other but only rely on each other’s rationality producing the optimal strategy.

Of course this relationship cannot last forever because it’s limited by many factors, e.g. participants’ lifespans, risk-free rate, VC risk tolerance, VC risk/reward, disruption of the technology utilized, company maturity level etc. And the best actual outcome players might hope is finding and executing their subgame Nash equilibrium where players’ returns would be better than greedy.

Although we can sometimes spot games and deduce optimal strategies on the macro level, applying them in the micro level where the actual life happens and decisions are made is much harder.

References

[1] KPMG Q4’20 Venture Pulse Report

[2] PitchBook 2020 Annual European Venture Report

[3] Prisoner’s dilemma, Wikipedia