Computer Simulation Studies of the Entrepreneurial Market Process

Abstract

This chapter reviews a line of research that studies several different theoretical questions in entrepreneurship through novel applications of computer simulation. All of the simulation studies reviewed are based on a shared game-theoretical modeling framework that allows a high level of integration with existing theories. What made these simulations unique was their firm grounding in the theory of the entrepreneurial market process from Austrian economics, and the lack of previous simulation studies in the entrepreneurship field. The focus is on how and why the cooperative game theory framework was chosen, the justification and process of applying the simulation method and the lessons learned from doing so. The aim is to provide entrepreneurship scholars with a better understanding of where and why computer simulation may add something of value to their research as a tool for the analysis of complex systems. The reviewed studies involve artificial economies with a small number of agents, demonstrating that the emergence of complex macro patterns from micro behaviors does not require large numbers of agents.

Appendix: Overview of the Littlechild Model

While the use of cooperative game theory has proliferated in the strategic management field in recent years, the entrepreneurship field has not seen such activity. One particular contribution that has remained underappreciated in the literature (Foss, 2000) is Littlechild’s (1979b) paper titled ‘An entrepreneurial theory of games’ that aims to take a step in capturing some elements of the entrepreneurial market process as described in the Austrian school of economics within the characteristic function game framework. In this appendix, we take a closer look at this paper’s model, and consider how it may serve as a basis for further research. The paper is a mix of informal narrative accompanied by some formal modeling. While the formal modeling does not cover all of the subjectivism and process dynamics discussed in the narrative, it does provide a basic framework that may be built on.

Littlechild (1979b) starts the formal description of the model as follows (p. 155):

Let $\left(N,\;v\right)$ be a game in characteristic function form where $N=\left\{1,2, \dots,\;n\right\}$ is the set of players. Let $M=\left(1,\;2, \dots,\;m\right\}$, where $m<n$, be the subset of players who choose an active role, i.e., the entrepreneurs. Define an artificial entrepreneur (player 0) permanently offering the value $v\left(\left\{\boldsymbol{j}\right\}\right)$ to any player $j$ cashing-in alone.

Active players are those who may propose offers to other players. Their behavior in looking for opportunities and proposing offers in order to exploit them justifies their labeling as entrepreneurs in the Austrian sense. The remaining $n-m$ players are passive, meaning that they may only accept or reject offers proposed to them, and do not actively seek opportunities or propose offers to others. Non-zero values for single-player coalitions are not necessary, as the game can be zero-normalized. However, having these non-zero values helps in the intuitive understanding of why a player may choose not to form any coalitions with others. Littlechild continues (p. 155):

At the beginning of each period $t$, where $t=0,\;1, \dots$, let ${S}_i(t)$ denote the set of players already committed to entrepreneur $i$ and $A(t)$ the set of as-yet uncommitted players. These sets are disjoint but collectively exhaust the set of all players. That is, the collection $\left\{{S}_0(t),\;{S}_1(t), \dots,\;{S}_m(t),\;A(t)\right\}$ forms a partition of $N$.

The sets of committed and uncommitted players are updated by

$$ {S}_i\left(t+1\right)={S}_i(t){\displaystyle \cup }{B}_i(t), $$

(2)

$$ A\left(t+1\right)=A(t) - {\displaystyle \underset{i=0}{\overset{m}{\cup }}}{B}_i(t). $$

(3)

Thus we are presented with a concise algorithm to model the game as it is played out through time. The outcome of the game is (p. 157):

A partition of players into coalitions $\left\{{S}_0,\;{S}_1, \dots,\;{S}_m\right\}$, where ${S}_i={S}_i(T)$, and a payoff vector $\left\{{x}_1,\;{x}_2, \dots,\;{x}_n\right\}$ which distributes the value of each coalition amongst its members so that

$$ A\left(t+1\right)=A(t) - {\displaystyle \underset{i=0}{\overset{m}{\cup }}}{B}_i(t). $$

(4)

$$ {\displaystyle \sum_{j\in {S}_i}}{x}_j=v\left({S}_i\right) $$

(5)

The requirement that the ${S}_i$ sets form a partition of $N$, implies that no two entrepreneurs may deal with each other. When the game starts at $t=0$ no passive player has decided to cash in alone (${S}_0(0)=\phi$), entrepreneurs have no one but themselves in their coalitions (${S}_i(0)=\left\{i\right\}$, $\forall i\in M$), and so all passive players are still on the market ($A(0)=N\backslash M$). The game is completed at any point $t=T$ when $A(T)=\phi$. Littlechild then begins to go beyond the pure framework of the characteristic function game by explicitly describing a model of the market process (pp. 155–156):

At the beginning of each period, each entrepreneur offers a price for each uncommitted player, and each uncommitted player sets a reservation price. The uncommitted player is signed up by whichever entrepreneur offers the highest price for him, provided this price exceeds his reservation price; otherwise he remains uncommitted. Formally, let ${p}_j^i(t)$ be entrepreneur $i$’s offer to player $j$, defined for $i=0,\;1, \dots,\;m$ and $j\in A(t)$, where ${p}_j^0(t)=\boldsymbol{v}\;\left(\left\{i\right\}\right)$, and let ${r}_j(t)$ be player $j$’s reservation price, for $j\in A(t)$. Let ${B}_i(t)$ be the set of players acquired by entrepreneur $i$ as a result of the bidding in period $t$, so that ${B}_i(t)=\left\{j\in A(t)\;:\;{p}_j^i(t)\ge {p}_j^k(t),\;k\ne i,\;\mathrm{and}\kern0.35em {p}_j^i(t)\ge {r}_j(t)\right\}$. In case of a tie in bidding, allocate the player arbitrarily to one of the maximum bidders, so that the sets ${B}_i(t)$ are disjoint.

And payoffs are distributed as follows (p. 157):

Each passive player gets the amount which he accepted on joining a coalition, and the entrepreneur’s payoff is determined by the balance remaining, so that

$$ {x}_i\equiv v\left({S}_i\right)-{\displaystyle \sum_{\begin{array}{c}\hfill j\in {S}_i\hfill \\ {}\hfill j\ne i\hfill \end{array}}}{x}_j\kern0.5em \mathrm{f}\mathrm{o}\mathrm{r}\kern0.5em i=1,\dots, m. $$

(6)

Although Littlechild does not run a dynamic simulation of the game, the only remaining elements needed to actually run the game are the strategies of the players. The strategies of active players consist of who to offer to, how much to offer them, and how to revise these in each new period, while the strategies of passive players consist of how to set reservation prices and how to revise them in each new period until an offer is accepted. Littlechild does not determine any particular way for the passive agents to set reservation prices, stating only that if they eventually start decreasing their reservation prices by at least a fixed minimum amount in each period, the game is guaranteed to end in finite time. As for the entrepreneur’s strategy, Littlechild suggests that if the entrepreneur had a guess for the price it would take to attract each passive player, then the following method could be used for choosing who to offer to, and how much to offer them (p. 156):

Let ${\widehat{p}}_j^i(t)$ be the price which entrepreneur $i$ believes it necessary to bid to secure $j$’s signature, where ${\widehat{p}}_j^0(t)\equiv v\left(\left\{j\right\}\right)$. Let ${D}_i(t)$ be the set of additional signatures desired by $i$. By definition ${D}_0(t)\equiv A(t)$, and for $i=1,\dots, m$ obtain ${D}_i(t)$ as the solution to the optimisation problem

$$ \underset{D_i(t)\ }{ \max }v\left({S}_i(t){\displaystyle \cup }{D}_i(t)\right)-{\displaystyle \sum_{j\in {D}_i(t)\ }}{\hat{p}}_j^i(t) $$

(7)

$$ \mathrm{subject}\ \mathrm{t}\mathrm{o}\ {D}_i(t)\subseteq A(t). $$

(8)

…Finally, set

$$ {p}_j^i(t)=\left\{\begin{array}{c}\hfill {\hat{p}}_j^i(t)\kern0.5em for\kern0.75em j\in {D}_i(t)\kern3.5em \hfill \\ {}\hfill 0\kern2.5em for\kern0.75em j\in A(t)-{D}_i(t).\hfill \end{array}\right. $$

(9)

Littlechild does not determine any particular way by which entrepreneurs may arrive at their guesses or revise them, although some suggestions are implied in that paper’s narrative arguments. Note that there is no cost to making an offer, and no limit on the number of offers an entrepreneur can make in each period.