game theory: draw a diagram to show the dominant strategy of what they should do The year is 1778, and the Continental Army desperately needs to get…

The year is 1778, and the Continental Army desperately needs to get supplies through to their troops at Valley Forge. A caravan of four wagons has left Philadelphia and must decide how to proceed. All four wagons can take the eastern route to Valley Forge, or the wagons can split up and two can take the western route instead. (The western route is too slow for all four wagons.) 

However, British Redcoats have intercepted dispatches that indicate the caravan is on its way. The British commander has just enough time to deploy two groups of scouts. He must choose whether to deploy both groups to the east, in order to maximize chances of spotting the caravan there, or split the groups up and send one to the west instead. 

  • • If the entire caravan goes to the east and the British scouts also all go east, then the Redcoats will likely intercept and capture three of the four wagons. 
  • • If the entire caravan goes east but the British split up their scouts, only two wagons will likely be captured. 
  • • If the caravan splits up and the British concentrate both scout groups to the east, only one wagon will be intercepted and captured. 
  • • Finally, if both the British and the Continentals choose to split up, two wagons (one each direction) will likely be captured. 

Game Theory wasn’t around yet in the 1770s, but if you were to go back in time and use game theory to analyze 

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