# Distinguishing Between Different Terms in Economics

I have no background and Economics and am trying to teach myself about some basic things in Economics. For example, I am trying to understand the following terms:

• Nash Equilibrium
• Optimal Strategy

To illustrate these concepts, suppose we have the following game (I think the game I have created is called a "Stackelberg Game"):

• There are 2 players: Player 1 and Player 2
• There are 2 Coins : Coin A and Coin B
• Coin A has a 0.5 Probability of landing on Heads and a 0.5 Probability of landing on Tails
• Coin B has a 0.7 Probability of landing on Heads and a 0.3 Probability of landing on Tails
• If Coin A lands on Heads, a score of +1 is obtained - if Coin A lands on Tails, a score of -1 is obtained.
• If coin B lands on Heads, a score of -2 is obtained - if Coin A lands on Tails, a score of +3 is obtained.

In this game:

• Player 1 selects a coin and then flips this coin and records his score
• Next, Player 2 selects a coin and then flips this coin and records his score
• The player with the highest score wins

In this game, Player 2 always has an advantage. He see what coin Player 1 picked and select the more favorable coin based on the choice of Player 1.

• If Player 1 picked Coin B and got "unlucky", Player 2 automatically wins if he picks Coin A
• If Player 1 picked Coin B and got "lucky", Player 2 can only win if he also picks Coin A
• If Player 1 picked Coin A, regardless of Player 1's result - Player 2 should also pick Coin A if he wants to minimize his chances of loosing

In this game that I created, I am trying to identify the Nash Equilibrium, Optimal Strategy and Saddle Point :

• I am confused between the concepts of Nash Equilibrium and Optimal Strategies. Based on the analysis I provided above, it seems like the Optimal Strategy in this game is for both players to always select Coin A - Would this be the Nash Equilibrium?

Thanks!

• I am sure this is more appropriate in math.stackexchange.com Almost no thing here is economical. Commented Mar 18, 2022 at 20:10
• it's a sequential game so NE won't help much to understand it. The relevant equilibrium concept is subgame perfect equilibrium.
– user39962
Commented Mar 18, 2022 at 20:45