Some fun theoretical models of risky technological innovation race

Keywords: risky technological innovation and competition; safety-performance trade-off; R&D and innovation race; public safety risks

Introduction

[Knight, 1936] viewed contests, or races, as a fundamental element of economic life, stating:

“The activity which we call economic, whether of production or of consumption or of the two together, is also, if we look below the surface, to be interpreted largely by the motives of the competitive contest or game, rather than those of mechanical utility functions to be maximized.”

Races are situations in which an individual’s reward depends on his performance relative to others. In a race, the largest - and perhaps only - prize is awarded to the first participant to cross a well-defined finish line. Investment in research and development (R&D) for a given technological innovation usually has several of the characteristics of a race. In such a race to be the first innovator, firms have to decide about the optimal timing of their R&D investments taking into account the dynamic interactions between competitors.

In his classic book Capitalism, Socialism, and Democracy, [Schumpeter, 1942] emphasized the connection between market structure and R&D. While he argued that allowing the formation of monopolies is necessary to incentivize the innovation process, I reverse the point of view in this present analysis by investigating how innovation may influence market structure rather than the converse as it has already been largely studied in the clas- sic industrial organization literature ([Arrow, 1962]; [Kamien and Schwartz, 1982]; [Aghion and Howitt, 2005]) In fact, in recent decades, innovation race as a field of research has undergone profound changes both in terms of analytical interpretations and in terms of application areas. These upheavals in the field of innovation race are the starting point for my reflection.

Specifically, I take as given the target of innovation and do not study the innovation’s impact on the broader economy from a macroeconomic perspective such as studying its impact on growth ([Aghion and Jaravel, 2015]; [Aghion et al., 2001]). The rationale behind taking a pure game-theoretical point of view – and its adjacent fields such as market design, e.g mechanism design or auction and contest theory – is that given the basic features of a race, game theory provides a suitable framework to study such strategic decision-making and is a powerful tool to analyze the risks and rewards of competitive innovation, both for the individual players and for the society as a whole. Behind this first consideration, the incentive to cut safety in a technology race mirrors obviously the temptation to defect in the prisoner’s dilemma. Indeed, while risk in the economics of innovation has almost always been seen trough the firm’s interest ([Mata and Woerter, 2013]), competitive technological innovation can also create public safety risks, as the pursuit of innovation and profit can sometimes lead to companies ignoring or downplaying potential risks associated with their products or services.

Starting from these distinctions, I break down the analysis into separate issues. First, in section one, I review the economics literature that gives insights on (i) the link between innovation race, market structure and its different interesting models (usually game-theoretic ones) and (ii) on public risk externalities created by innovation race - and in particular by AI race. In section two, I give some basis to model simple technological innovation race and focus once again on an AI race through a Do It Yourself (DIY) proposition.

1. Literature review on innovation race

1.1 Classical game theoric innovation race

There has been a significant amount of research conducted by economists since the 1970s on the topic of technological competition between firms, with the development of various “racing” models to explain this phenomenon. The classical industrial organization literature usually predicts that, in an innovation race, asymptotically, the economy converges to concentration or dominance of a single firm, i.e a monopoly. However, depending on the theoretical conceptualization of rivalry and on whether the model is deterministic or stochastic, several papers offer sharply different predictions by showing that this increasing dominance outcome can be challenged by an “action-reaction” effect.

[Horner, 2004] finds that it is not necessarily true that competition is fiercest when competitors are close, as could be suggested by some existing models of [Aghion et al., 1997]. The model of Horner seek to extend the classical first model of [Aoki, 1991] by assuming that the technology is not restricted to being deterministic, i.e. an investment level generates a probability distribution over outcomes! The most significant factor is the joint profit effect, which refers to the idea that on average, the joint profits from the product market are higher when the gap between the firms grows rather than shrinks. This leads the leader to put in more effort than the laggard. This joint profit effect is relatively well understood and is the driving force behind traditional analyses of patent races ([Grossman and Shapiro, 1987], [Harris and Vickers, 1987]; [Loury, 1979]).

Indeed, patent race is a very important part of literature when it comes to competitive innovation. In these papers, the joint profit effect typically supports increasing dominance, with the leader tending to get further ahead over time. The classical work of [Loury, 1979] on patent race has been largely extended ([Lee and Wilde, 1980], [Reinganum, 1982]). In such memoryless R&D race models, the knowledge that firms have acquired as a result of their past R&D efforts is irrelevant to their current R&D efforts. The rationale behind this strong assumption is that the time of a successful innovation is exponentially distributed.

However, some models aim to overcome the memorylessness property of traditional R&D race models. Multistage race models are designed to account for the influence of past events on the competition by introducing intermediate steps in the research process. In these models, a firm must complete all stages of the R&D project in order to win the race. Deterministic multistage race models assume that firms move from one stage to the next in a predictable way ([Fudenberg et al., 1983]; [Lippman and McCardle, 1988]). An other important contribution is due to [Doraszelski, 2003] where his model does not take into account this memoryless property and finds that under some conditions, the firm that is behind in the race engages in catch-up behavior.

An other part of the literature that study innovation race is economic models of auction ([Grossman and Shapiro, 1987]). [Siegel, 2009], study “all-pay contests” which capture general asymmetries and sunk investments inherent in scenarios such as R&D races. All-pay contests or auction are contests in which every bidder must pay regardless of whether they win the prize, which is awarded to the highest bidder. In many settings, economic agents compete by making irreversible investments before the outcome of the competition. Innovation races are an example in point.

In a nutshell, when comparing deterministic, the auction and stochastic racing models, the resulting equilibrium outcomes can sometimes be significantly different. Given these potential variations in results, it is crucial to select the appropriate paradigm. The stochastic racing model appears to better capture the nature of R&D, which may or may not yield a successful outcome and can require more or less time and resources than anticipated. In the case of development or introducing a new product, the auction model may be the preferred choice if the technological uncertainties have already been resolved.

1.2 Innovation race with safety compliance

The public safety risks created by competitive innovation are understudied in the economics literature. There are two aspects of innovation that together create a risk externality: (i) innovating creates a risk of widespread negative consequences if agents under-invest in safety, but (ii) developing safely is costly for the agent by placing it behind in an innovation race. Under certain conditions, the twin effects of widespread risk and costly safety measures may cause a “race to the bottom” in the level of safety investment. In a race to the bottom, each competitor skimps on safety to accelerate their rate of development progress.

The Collingridge Dilemma highlights the challenge of predicting and controlling the impact of new technologies, especially in the field of AI. Due to the lack of available data and the inherent unpredictability of this technology, it may be beneficial to use a modeling approach to gain a better understanding of the potential consequences of a race for powerful AI systems. Thus, the case of an AI race is interesting for several reasons. Firstly, the risk of negative externalities is inherent to the development and implementation process itself ([Armstrong et al., 2015]) . Thus, one can think of this as an endogenous deadline rather than an exogeneous one (i.e a well finished deadline) as it is almost always the case in the traditional race literature. Secondly, risky technological races and more particularly the AI race differ from traditional arms races in several ways. Arms races typically conclude with the declaration of war, while technology races may end either when (i) one party successfully develops the technology or (ii) when too much risk has been taken, and a disaster has occurred. Furthermore, the AI race and its associated risks are particularly distinctive from any other technological race (cf. work of the Centre for the Governance of AI).

Most of the race models we have seen so far only allow for two players, which is obviously quite restrictive. Thus, some papers in the literature stand out by investigating innovation race trough network games. [Cimpeanu et al., 2022] enlighten the fact that it is important to understand how diversity in the network (different collaboration networks eg. among firms, AI researchers, stakeholders etc.) influences race dynamics as some players might play a pivotal role in a global outcome. They examine various network structures, including homogeneous ones like complete graphs and square lattices, as well as various scale-free networks that represent varying levels of diversity in the number of co-player races a player can participate in. As in the case of climate change games ([Santos and Pacheco, 2011]), the perception of risk is a key factor driving the evolutionary outcome (whether or not disaster happens).

The role on information as it has already briefly been stressed above is crucial to determine the race dynamics. [Armstrong et al., 2015] find, counter-intuitively, increasing the information available to all the teams (about their own capability or progress towards AGI, or that of the other teams) increases the risk of a catastrophe. Their results alos show that competition might spur a race to the bottom if there are too many teams.

[Naudé and Dimitri, 2018] try to see what kind of public policy mechanisms (introducing intermediate prize, taxation, public procurement of innovation, patent) to implement in a risky technological race such as an AI race in order to safely control the nature of AI. The authors found that the intention of teams competing in an AI race as well as the possibility of an intermediate outcome (prize) is important when considering safety levels.

In a nutshell, it seems that even though there has been minimal focus on analyzing the dynamics of emerging risky technological race such as an AI race, such models offer sharply different predictions on (i) how a firm’s tendency to innovate in a race is impacted by its technological position relative to the others competitors in a given network structure and the level of information openness in the race and on (ii) how the “safety-performance” trade-off might evolve over the race.

2. DIY your own AI race game

What are the main characteristics, parameters and variables to consider of an AI race? One could think of different hypothetical scenarios and conditions of the race concerning:

• disaster risk,
• risk-perception behaviours,
• level of information openness,
• number of racing teams,
• level of heterogeneity of teams’ development capacity
• incentives deployment,
• entry cost,
• types of teams (AI gov lab, private firms, collective eg. Stable Diffusion),
• network of teams (i.e from a more macro and structural perspective, the different ties racing teams might have through the network topology)

I hope that the literature review written above has already given the reader some ideas of concepts and methods to be used to model an AI innovation race but the main tools remain probably game theory, networks and computational methods such as agent-based modelling. However, I have still a too narrow view on AI governance to say how important and influential the present parameters and variables are on the results of an AGI race. Still, since companies play currently an outsize role in AI R&D compared to academic or government groups/labs, the need to focus on corporate governance seems to be a crucial thing to consider for AI governance people.