Consider a large hospital and small physician group who are considering merging practices (vertical integration).

Vertical integration in this setting may potentially be beneficial if the organizations are able to share patient referrals, coordinate better, establish continuity of care with less effort, and negotiate higher reimbursement rates with insurance companies. However, pursuing the acquisition is also potentially costly in terms of time and effort courting the other group, as well as resources spent satisfying legal and regulatory requirements.

If neither choose to pursue the acquisition, the hospital will earn $100M and the physician group will earn $10M.

If the hospital pursues the acquisition and the physician group decides to remain independent, this result is very costly to the hospital who had to spend $10M taking the physicians out to dinner and forgoing other opportunities during the merger talks. However, the physicians benefit from these dinners and can be more productive, earning $2M more than they would have otherwise.

If the physicians want to merge with the hospital but the hospital does not want to acquire the physicians, this outcome will cost the hospital nothing (no change in payoff), but the physicians will benefit from the additional networking they did with the hospital, earning them $1M more than they would have otherwise as the hospital sends a few additional patients their way.

Finally, if both the hospital and physicians decide to proceed with the merger, the hospital gains an additional $10M in net profits (above and beyond resources spent on physician dinners and other costs during the negotiations). The physicians also see substantially more patients and now earn $5M more than normally expected.

Objectives:

1. We can describe the scenario above as a simultaneous move game. Who are the players and what are their potential strategies?
2. Represent the players, strategies, and payoffs described above in a normal-form game.
3. Does the physician group have a dominant strategy? Explain/discuss.
4. Does the hospital have a dominant strategy? Explain/discuss.
5. Identify any Nash Equilibrium(s) and discuss what you predict will happen in the above scenario.
6. How would the game described above differ if it had been a sequential move game rather than simultaneous? Do you expect that it would have changed the outcome? Do you think it would matter which player moved first? Discuss.