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Game Theory Analysis

Help for game theory analysis in the real options valuation template for Excel

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Real Options Valuation Help Topics: Option Pricing Fundamentals The Option to Delay a Project The Option to Expand a Project The Option to Abandon a Project Binomial Option Pricing Game Theory Analysis

The Game Theory model utilizes real option pricing and Nash equilibrium to calculate the expected strategy and payoff for two firms in a competitive environment. The information provided from such an analysis is extremely useful to evaluate proposals to enter a competitive market.  The models works by evaluating each firm's optimal strategy in order to launch the product or service in the market (exercise a call option) in relation to its competitor. Each firm can be either, a leader (enter the market first), a follower (enter after), or both firms could enter simultaneously. The model calculates the probabilities for each of these scenarios and the resulting expected payoff.



On clicking the 'Start' button in the 'Menu' sheet; you are taken to the 'Game' sheet.  Inputs are entered into the cells highlighted with a light blue color. Assistance for both input and calculated parameters can be sought by selecting the relevant cell and clicking the Help button to the right. The key inputs required for the model are:

  1. If similar projects or investments have been undertaken or made in the past the standard deviation of cash flows resulting from these projects can be used as a proxy for the standard deviation in cash flows for the proposed investment.
  2. Probability analysis can be run on simulations of key inputs, such as revenue and cost drivers, market size and market share, to estimate the standard deviation of the resulting present value. While this type of analysis can be accomplished by using sampling analysis in the Analysis ToolPak add-in shipped with Excel, third-party add-ins can facilitate more sophisticated applications.
  3. The standard deviation of publicly traded firms in the same business or industry can be used a proxy for the proposed investment.  This is the least preferred method due to the likely diversity of activities undertaken in other firms and resulting differences in variance characteristics. Such industry specific volatility data can be obtained from third party market data providers (such as those recommended at the Business-Spreadsheets.com web site) and entered into the Pre-Defined sheet for future use across models and proposals. It should be noted that the Pre-Defined sheet can also be utilized to store standard deviation data from similar projects undertaken in the past as described in the first method.


Parameters are calculated from these inputs to drive the analysis. These are:


Sensitivity Table

Below the main parameters section is a table displaying the strategy probabilities and resulting expected payoff for different levels of annual cash flow in the market.  The first row shows the expected level of market cash flows and corresponding results. Next, two rows show levels of annual market cash flow is below the level where leading equals following. In this case, each firm will wait until cash flow reaches this level, which is displayed underneath.


Below this two more levels of annual cash flow are shown greater than the level where leading equals following and less than the level where it pays to follow.  In this region, each firm will consider leading and the probability to exercising increases as the level of cash flows available increases.


Finally, the level of annual market cash flows where it pays to be a follower is displayed with two levels greater than this underneath. For these levels, both firms with enter the market immediately and simultaneously.


Results Summary

Below the sensitivity analysis is a textual summary of results for the expected annual level of market cash flows. This provides an explanation of each of the key parameters, strategy probabilities for each firm, and resulting expected payoff. This summary can be useful for direct insertion into business case proposals and reports.

Screenshot: Game Theory Analysis