Liberal Democrats are to begin “war gaming” scenarios for a hung Parliament as they consider overtures from the Conservatives to change the electoral system to permanently disadvantage Labour.

Small groups of senior Lib Dem MPs believe that there is a good chance that the next election will see no party with an overall majority, meaning that Nick Clegg’s party could be asked to act as “kingmaker”.

It intends to prepare for various contingencies using the principles of game theory developed by the Nobel prize-winning mathematician John Nash and regularly employed by the CIA.

This technique, where “mind trees” outlining various scenarios are drawn on whiteboards, was used by Vince Cable for many years when he was chief economist at Shell. Together with Chris Huhne, then a City analyst, they mapped out possible scenarios concerning political stability in Nigeria and the future of Norway’s regulatory framework.

The whiteboards are still a prominent feature in the Westminster office of Mr Cable, now Liberal Democrat Treasury spokesman and deputy leader.

There is little enthusiasm among Liberal Democrats at every level of the party to support a Tory government, despite increasing overlap in some policy areas.

“A lot of us see Labour as the competition and the Tories as the opposition,” one senior party figure said, adding that the personal chemistry between David Cameron and Mr Clegg is poor.

However the top of the party is also united in its belief that they must remain “equidistant” from both Labour and the Tories in order to maximise their negotiating hand in the event of a hung Parliament.

They recognise, for instance, that it would be “suicide” for the party if it kept Gordon Brown in Number 10 in the event that the Conservatives emerge as the largest party.

The scenarios will also include planning for what to do if a minority government dissolves within months and there is a second general election, throwing up a whole new set of choices.

“It is impossible to predict. The situation will be dynamic,” said one insider. “What you have to remember is in the top three we have Nick and Chris, who are experienced negotiators, and under Vince Cable Shell’s economics team specialised in scenario planning to prepare for eventualities.” The party’s legal experts say that the laws governing the procedures for a hung Parliament are confused and contradictory, and could even open the way for Gordon Brown to try and cling on to power if the Tories formed the largest party.

The party is openly putting together a manifesto that would form the basis of their negotiations. At this weekend’s Spring Conference in Harrogate, members approved plans for a £7 billion cash injection into schools and childcare, paid for by cutting tax credits to middle and high earners.

Proportional representation is seen as an important part of the package but will not be a deal breaker for the party, since this would advantage Labour who are believed to be much readier to concede PR than the Conservatives.

The Tories are also quietly trying to persuade Liberal Democrats to give them backing for two changes they would make in the event they won a general election. Mr Cameron has already signalled he wants to redraw the boundaries to reduce the number of seats in a way which could hurt Labour, and has been open on his desire to change the rules to limit union funding. The Lib Dems have yet to reach a conclusion on these issues.

Personal relations between the Tory and Liberal Democrat leaders are cool, according to his colleagues. Shortly after his election last year Mr Clegg and his wife Miriam were invited for dinner at Mr Cameron’s home. He declined, sensing that this could store up problems in the future. Subsequently the Lib Dems think that Mr Cameron has behaved “dismissively” towards Mr Clegg.

Mr Clegg would have to get the approval of the wider party to any deal after rules introduced during the Nineties to hinder Paddy, now Lord Ashdown from doing a deal with Tony Blair without securing wider agreement. Insiders are relaxed about this, recognising that it would help quell inevitable internal dissent.

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