Explain Game Theory and draw an example of a matrix. Please phrase things clearly/simply so I can understand, as I am still fairly new to economics. Thank you!!
Game Theory is an extremely wide concept which cannot be fully understood with just one example. I'll try to explain what a payoff matrix is and how to find a Pure Strategy Nash Equilibrium using some examples. I'll also explain what these terms mean.
Say, we are playing the following game:
Two cars are approaching each other from opposite directions. They both have a choice of either going left or right. Let's call the cars Car A and Car B. If Car A goes left and Car B goes right, both cars collide and receive a payoff of (-10) each. Payoff is the return from choosing a particular strategy. If car A goes left and Car B also goes left, both cars receive a payoff of (10) each. If Car B goes left and Car A goes right, both cars receive a payoff of (-10) each. If Car B goes left and Car A also goes right, they end up in wrong lanes and receive a payoff of (0) each.
We can represent this game in the form of a payoff matrix as follows:
Car A/B | Left | Right |
Left | (10,10) | (-10,-10) |
Right | (-10,-10) | (0,0) |
Car B is the column player and Car A is the row player. We have just represented the problem in the form of a table which represents each player's payoff from playing a particular strategy. For example, if we want to know what is the players' payoff when Car B goes left and Car A goes right, we have to look in the first column and second row of the table to find the entry (-10,-10).
The solution of this game would be a strategy which would be followed by both players which would give them the highest payoff out of all the available strategies.
Let's start with Car A. If Car B plays left, Car A has a choice of playing left or right. Playing left gives Car A a payoff of (10) and playing right gives Car A a payoff of (-10). Hence, when Car B plays left, Car A will always play left. This can be done for the situation when Car B plays right. When Car B plays right, Car A will always play right to receive a payoff of (0).
We highlight Car A's best strategies:
Car A/B | Left | Right |
Left | (10,10) | (-10,-10) |
Right | (-10,-10) | (0,0) |
Now, for Car B. If Car A plays left, Car B can play left or right. To maximize payoffs, Car B will play left when Car A plays left. If Car A plays right, Car B will play Right.
Now we highlight Car B's strategies:
Car A/B | Left | Right |
Left | (10,10) | (-10,-10) |
Right | (-10,-10) | (0,0) |
Therefore, this game has two Nash Equilibria. This kind of Nash Equilibria is known as a mixed strategy Nash Equilibria. It requires some additional knowledge of probability to arrive at the final answer. But since these are the very basics of Game Theory, learning the process of finding Nash Equilibria is a good place to start.
Nash Equilibrium is a state where none of the players have an incentive to change their strategies and are receiving the maximum payoff possible given the responses of other players.
Explain Game Theory and draw an example of a matrix. Please phrase things clearly/simply so I can...
True or False: Please explain why this is true or false so I can understand. Just part b. Thank you taneous move stage game, then there cannot be an SPNE of the infinitely repeated game in which player i plays D every period (b) In any Nash equilibrium of an infinitely repeated game, the players play one of the stage game Nash equilibria in every period.
can u please help me answer this question and also please write clearly so I can understand thank you 18. How do cels know where to send a parti orgmnells? 19. How do cells know a given protein is transmembrane protein, or soluble?
How many isomers of 1,6-heptadiene exist? (Answer is one, but please draw so I can understand) How many isomers of 1,3 heptadiene exist? (Answer is two, but please draw so I can understand) How many isomers of 1,3,5-heptatriene exist? (Answer is four but please draw so I can understand) Thank you, will rate asap
5. Explain what is meant by the phrase the Fisher Effect. Please draw 2 clearly labelled separate graphs, one with the nominal interest rate and the other with the real interest rate.
Please include detailed explanations so that I can clearly understand how to solve these problems. Thank you! 3) Draw the structure, showing the stereochemistry, of the chiral products A, B and C. tBuOK CH2SO2CI 2 B он NaCN rate = k [B][NaCN] 4) Draw the structure of the two products resulting from the following reaction. What is the realtionship between these two products? Br LDA rate = k [D][LDA] Br D Relationship:
Please write clearly so I am able to follow the steps and understand how this problem is done. Thank you! 5. A sphere weighing 2.5 kN has a radius of 0.15 m. What forces does the sphere exert on the inclined surfaces? W-2.5kN 30 75
please help me answer this question and also please write clearly so I can understand thank you so much also please show all steps thank you so much Q4 On mountainous downhill roads, escape routes are sometimes placed on the side of the road for t Assuming a constant upward slope of 26, calculate the horizontal that slowed from 110 km to rest in 7.0 seconds. (see proble Ch 3, page 72, #53). rucks whose brakes might fail. and vertical...
can u please help me answer this question and also please write clearly so I can understand thank you so much also please show all steps thank you so much Q1 The following formula estimates an average person's lung capacity V (in liters, where 11-103 cm): V = 4.1 H-0.018 A-2.7 where H and A are the person's height (in meters) and age (in years), respectively. In this formula, what are the UNITS of the numbers 4.1, 0.018, and 2.7?...
Please explain the answers so I can understand, thank you. + 5 μC is located at (0, 0.40) m, which is at the y axis and 0.40 m from Q2. the origin. A negative charge q2 =-2 is located at the x axis, 0.30 m from the origin. Find the magnitude of the force in between these two charges. (worksheet problem) (Simply use ke-9.0x10 Nm A positive charge q 2/C?. You should know that 1pC- 10 *C)
PLEASE explain why and show work so I can try to follow and understand!! Thank you!!