1. 1 Game theoretic approach to unlicensed spectrum radio resource mgmt. Olav Queseth olav@radio.kth.se

2. 2 10 minute game theory intro Zero-sum 2 player games Players Strategy Payoff Police You Road Forrest RoadForrest 0 1 1 0.5 Escape probability

3. 3 Game theory in radio Player – Someone who plays the game n users or n operators Strategy – A set of possible actions a player can make User: Select waveform, transmission power, timing etc. Operator: Select which users to assign what to Payoff – The reward from the game User: Datarate, power consumption, error probability Operator: Revenues, user satisfaction etc...

4. 4 Complications Utility Is not always easy to assess the perceived value of a payoff More than two players You don’t even have the power of making life misserable for your opponent... Non-zero sum Partially the same objective as your oponent

5. 5 Power game example – players and utility G 11 G 21 G 22 G 12

6. 6 Strategy and payoff 2 BS, user in the middle, 20 dB at other BS Rate proportional to C/I P 1 [dBm] P 2 [dBm] R 1 [dB]

7. 7 Nash equilibrium Reaction function

8. 8 Nash equilibrium P2P2 P1P1 Player 2’s reaction function Player 1’s reaction function Nash equilibrium P max

9. 9 Timeslot game Additional rules: Two timeslots Energy constraint 1 2 P1P1 P2P2 TT

10. 10 Payoff Users use all available power:

11. 11 Nash Equilibrium

12. 12 Nash Equilibrium P 21 P 11 High throughput Low throughput

13. 13 Extensions in the works Rate as a log function More than two (users, timeslots) More complicated games Repeated games – can encourage cooperation Cooperation, contracts and coalitions

14. 14 Final remarks Game theory is a powerful tool for analysis Utility is a tricky assumption It makes sense to use all power in one slot (if there is an energy constraint) These simple games (that can be analysed) may be too simple